The Ross–shire MSP will self-isolate for up to 10 days because she received her second dose of a coronavirus vaccine less than two weeks ago, she said.
Announcing the news on Twitter, Ms Forbes said would continue to work from home.
“Late this afternoon, a family member tested positive,” she tweeted.
“As a close contact, I will now self-isolate for the full period as I am not fully vaccinated (it’s been less than a fortnight since my second vaccine).
“I will still give evidence at two committees tomorrow and respond to the debate on the McVitie’s closure at Tollcross, amongst many other commitments this week and next, albeit virtually.”
It follows a brief spell in self-isolation for Nicola Sturgeon, who was also recently identified as a close contact of an infected person but was able to stop isolating after testing negative.
The Scottish First Minister said on Monday morning that she was “relieved” by the results of the PCR test.
Under the current rules in Scotland, close contacts and children are able to end isolation if they are symptomless, have returned a negative PCR test and if they have been double-vaccinated for at least a fortnight.
But anyone who does not meet those criteria must isolate for 10 days from the point an infected person developed symptoms, regardless if they have symptoms themselves or test negative.