Maree Todd revealed on social media that she had received a positive test result on Tuesday and that she was self-isolating at home with her family.
The SNP MSP for Caithness, Sutherland and Ross has been the Minister for Public Health, Women's Health and Sport since May's election.
She said she was not suffering any coronavirus symptoms and praised medical and public health staff.
She said: "I've received a positive Covid test result today. No symptoms but am obviously self-isolating with my family now.
"I also want to say thanks to the testing staff and the contact tracers for their work.
"They are on the frontline and are magnificent. Thank you all."
Health Secretary Humza Yousaf also tweeted: "Sorry to hear my friend & colleague Maree Todd MSP has tested positive for Covid.
"Best wishes for a speedy recovery for her and her family."