The House of Commons speaker has said he is "very, very angry" at the "reckless" behaviour of an MP who travelled from Glasgow to London with Covid-19 symptoms, then returned home after testing positive.
Sir Lindsay Hoyle said he could not believe that Margaret Ferrier had put other people's health at risk.
And he said she had not initially given a straight story to the authorities.
Ms Ferrier has been suspended by the SNP and faces calls to quit as an MP.
DUP MP Jim Shannon, who was seated at the same socially-distanced dining table as Ms Ferrier on Monday evening, is self-isolating but received a negative test result on Thursday afternoon.
An Assistant Serjeant at Arms was close to Ms Ferrier when she spoke in the Commons on Monday but has not been advised to self-isolate.
Ms Ferrier has apologised and said she "deeply regretted" her actions but has not yet given any indication of whether or not she intends to continue sitting as an independent MP.
She has referred herself to the Parliamentary Commissioner for Standards, as well as to the police.
Scottish First Minister Nicola Sturgeon, who is also the SNP leader, told her daily coronavirus briefing that Ms Ferrier had been guilty of the "worst breach imaginable".
And she said she had made it "crystal clear" to her that her "reckless, dangerous and completely indefensible" actions meant she should stand down in the interests of the overall integrity of the public health message.
When asked by the BBC whether he believed Ms Ferrier should quit as an MP, Sir Lindsay replied: "I would expect the member to consider what they have done, and the reckless behaviour, and how that looks to the rest of the country.
"This sends all the wrong messages. People have really got to consider their position on that."
The Speaker expressed his "complete shock that somebody could be so reckless" and said he was "really very, very angry" that "the House has been put at risk".
He said Ms Ferrier had then put "a whole different set of people at risk" by travelling on public transport after testing positive for the virus.
He also criticised the speed at which he was informed about the incident - but blamed the MP, rather than the SNP.
Sir Lindsay said: "Not to be told until Wednesday is not acceptable, and we were hearing different stories, different messages, that made it even more difficult to deal with."
Ms Ferrier, the MP for Rutherglen and Hamilton West, said she had experienced "mild symptoms" on Saturday and was tested for coronavirus.
However, she decided to travel by train to Westminster on Monday before getting her result because she was "feeling much better".
She spoke for four minutes in the Commons chamber during a coronavirus debate - tweeting a video of her speech - but was told later that evening that she had tested positive for the virus.
Despite this, Ms Ferrier took a train back to Scotland on Tuesday, with SNP whips in the Commons being told about her positive test on Wednesday.
It is understood she had initially told the party she was going home because a family member was unwell.
A spokesman for the party said the SNP's chief whip immediately informed parliament authorities after learning of Ms Ferrier's positive test on Wednesday.
But he said it was not until Thursday that the SNP discovered that Ms Ferrier had been tested prior to travelling to London and had then travelled back to Glasgow despite knowing that she had a positive result.
Ms Sturgeon said she was only told on Thursday afternoon - shortly after she faced opposition leaders at first minister's questions in the Scottish Parliament.
Ms Ferrier's actions became public when she tweeted an apology at about 18:00 on Thursday.
SNP sources initially said they would await the result of a police investigation into her actions before deciding whether or not she would be suspended.
But the party announced her suspension about an hour later, with Ms Sturgeon subsequently tweeting that the MP's actions had been "indefensible".
I’ve spoken to Margaret Ferrier and made clear my view that she should step down as an MP. I did so with a heavy heart - she is a friend & colleague - but her actions were dangerous & indefensible. I have no power to force an MP to resign but I hope she will do the right thing.— Nicola Sturgeon (@NicolaSturgeon) October 2, 2020
Police Scotland confirmed they had been contacted by Ms Ferrier, saying officers were "looking into the circumstances" and liaising with the Metropolitan Police Service.
Ms Ferrier could face a £4,000 fine for a first-time offence of coming into contact with others when she should have been self-isolating under a law that came into force on the day of her positive test.
Ian Blackford, the SNP leader at Westminster, earlier told BBC Breakfast that "nobody is above the law" and calling on Ms Ferrier to "do the right thing".
SNP MPs David Linden, Kirsty Blackman and Stephen Flynn have also called for her to step down.
BBC Scotland's chief political correspondent, Glenn Campbell, said there may be a way for Ms Ferrier's constituents to force her out if she refuses to quit.
This would require her to first be suspended from the Commons for a fortnight or ten sitting days by the standards committee.
If 10% of registered voters in her constituency then signed a recall petition within the next six weeks, her seat would become vacant and a by-election would be called.
Five days a week, every week, Nicola Sturgeon appears on TV, taking questions about her coronavirus policies and urging every one of us to abide by the rules.
So for the MP who has committed the most egregious breach of the regulations - possibly of the law - to be one of her own is acutely embarrassing.
The SNP leader who has been quick to condemn others for breaking the rules has made no attempt to defend or excuse Margaret Ferrier.
This is the first minister whose chief medical advisor resigned for breaking lockdown rules back in April and who demanded the sacking of the PM's chief advisor Dominic Cummings after he admitted to breaches of the regulations.
She swiftly condemned Margaret Ferrier's behaviour as "utterly indefensible".
SNP MPs called publicly Ms Ferrier to resign and Ms Sturgeon has spoken to her this morning and made clear that she should step down as an MP.
But the problem for the SNP is that they cannot force the MP for Rutherglen and Hamilton West to leave her job. They have already removed the party whip and suspended her from the SNP. But that is all they can do.
Ms Ferrier was one of the MPs who called on the prime minister's adviser Dominic Cummings to resign in the wake of the controversy over his visit to the North East of England during lockdown.
At the time, she said his actions had "undermined the sacrifices that we have all been making in lockdown to protect each other from coronavirus" and described his position as "untenable".
Scottish Conservative leader Douglas Ross said Ms Ferrier's "reckless" actions had put the lives of other people at risk, and has questioned the SNP's timeline of events.
Mr Ross said: "The SNP say they only found out about any wrongdoing on Thursday. That means we're supposed to accept that the SNP found out Margaret Ferrier tested positive on Wednesday - and asked nothing.
"The SNP's timeline is full of holes and any reasonable person can see that."
Shadow Scottish secretary Ian Murray also demanded answers from the SNP to the "very serious questions" surrounding the behaviour of Ms Ferrier.
The Scottish Labour MP said her "catastrophic, negligent actions" had put lives at risk.
Ms Ferrier was first elected as an SNP MP in 2015 but lost her seat to Labour in 2017 before winning it back in last year's general election with a majority of 5,230.