A pharmacy in Inverclyde is among a number of businesses which have been linked to a new coronavirus cluster.
Eight positive tests in Port Glasgow are among 14 new cases reported in the Greater Glasgow health board area.
NHS Greater Glasgow and Clyde said none of the cases were experiencing anything more than mild symptoms.
It added: "Close contacts are being advised to self-isolate and other identified contacts are being followed up and given appropriate advice."
Greenock and Inverclyde MSP Stuart McMillian tweeted to say he would not speculate "where or who is involved".
But he said: "News has broken that there has been a cluster of Covid-19 cases in Port Glasgow.
"I have spoken to the Scottish government and the health board, and their Track and Trace Investigation Team are working on this as we speak.
"I will share information to help the community when I get it."
First Minister Nicola Sturgeon confirmed that an incident management team was meeting to discuss the development.
The cases were among 22 reported across Scotland in the last 24 hours.
Ms Sturgeon has previously said localised outbreaks of the virus are all but inevitable, following clusters in North Lanarkshire and Dumfries and Galloway.
However, the first minister said the "test and protect" system was working well, with the number of people being treated in hospital for Covid-19 remaining low.
Ms Sturgeon said: "Part of the challenge we have around any potential cluster is to make sure everything possible that can be done to minimise onward transmission is done."
The first minister said people should be assured that "any suggestion of any links between cases or possible clusters or outbreaks are absolutely rigorously explored, investigated and dealt with".
News of the cluster came as the National Records of Scotland said the number of deaths linked to coronavirus had increased very slightly, with Covid-19 mentioned on eight death certificates in the week to Sunday.
This was an increase of two deaths from the six that were recorded the previous week.
Ms Sturgeon said numbers were likely to fluctuate at such a low level, pointing out that the overall number of deaths in Scotland was below the five-year average.
However she said her government was likely to "adopt a very cautious approach" at the next review of lockdown restrictions on Thursday.
She said "very significant changes" had been made in recent weeks, with the hospitality and tourism industries reopening, and said it was "still too early to be completely assured" of the impact of this.
Ms Sturgeon said it was important not to "do too much too quickly and give the virus the chance to overwhelm us again".
The first minister is expected to give further details of when and how Scotland's schools will re-open on Thursday.