His positive test came on the same day that Russia recorded a record 7,099 cases, taking the total number of infections above 100,000.
Mr Mishustin was given the role of prime minister in January and has been actively involved in Russia's handling of the epidemic.
Russian TV showed him telling President Vladimir Putin of his diagnosis.
"I have just learned that the test on the coronavirus I took was positive," the prime minister said during the video call.
Mr Mishustin suggested that First Deputy Prime Minister Andrei Belousov should take his place and Mr Putin agreed. Mr Mishustin will now go into self-isolation.
"What's happening to you can happen to anyone, and I've always been saying this," Mr Putin told him.
"You are a very active person. I would like to thank you for the work that has been done so far."