Ex-Tory minister Anna Soubry says her office has received 13 death threats since a newspaper front page named her as one of 15 "Brexit mutineers".
The pro-EU Remain supporter said the police took the threats seriously and had passed two cases to prosecutors.
She said she had been "really quite frightened" and blamed the threats on Wednesday's Daily Telegraph front page.
The paper's editor defended what he called "the legitimate actions and language of a free press".
The story concerned Conservative MPs planning to rebel against the government's bid to enshrine the precise date of Brexit in law.
Speaking on Broadcasting House on BBC Radio 4, Ms Soubry said her office had told her of the 13 death threats.
"That's just astonishing, isn't it?" she said.
"The police take it seriously - it's not nice, it's not acceptable and it's not necessary."
Ms Soubry had previously described the headline as a "blatant piece of bullying".
The threats had included "references to what happens to mutineers", she told the BBC, adding: "A number of tweets have said we should be hung."
She added: "If the Telegraph had not printed that headline those death threats would not have come through - that is a fact."
The government lost its majority at the general election and risks defeat when the Commons votes next month on the Brexit date issue.
Speaking on the BBC's Andrew Marr Show, Chancellor Philip Hammond said the government would not be withdrawing its plans to press ahead with the move, adding that Parliament was "quite rightly" debating the proposals as part of the EU (Withdrawal) Bill.
'Absurd and shrill'
The BBC has contacted the Daily Telegraph for a formal response.
But in a tweet to Broadcasting House presenter Paddy O'Connell, editor Chris Evans said: "I'd urge you to distinguish between the legitimate actions and language of a free press and the illegitimate actions and language of those who make threats of violence."
He also referred to a leader article in Saturday's paper defending the headline, which it says was intended to be "arresting" and to show "that there are still forces at work seeking to stop Brexit happening".
It added: "The individuals may disagree with that observation, but we were entitled to make it and we will see during the course of the next year whether there is any merit in it.
"But the accusations of bullying are absurd and shrill."
The article also pointed out that Ms Soubry had described her inclusion in the front page as a "badge of honour".
The Telegraph's front page echoed that of the Daily Mail when it singled out three judges - labelling them "Enemies of the people" - after the High Court ruled that MPs must have a say on triggering Article 50.
The Daily Mail's piece attracted hundreds of complaints to watchdog the Independent Press Standards Organisation.