Scammers pretending to work for the Test and Protect contact tracing service have been cold-calling people and demanding payment for tests.
First Minister Nicola Sturgeon highlighted the emerging fraud during her daily media briefing.
She said the crime was “truly and utterly despicable” and issued a reminder that Covid-19 tests were free.
She added Test and Protect staff would never request financial information or attempt to secure payment for tests.
They will only ask about people’s movements and who they have been in contact with.
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Ms Sturgeon said: “Sadly there are always a small number of people, and it’s a tiny minority, who will try to exploit any situation they can to defraud people and it’s truly and utterly despicable particularly at this time of crisis.”