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."
Mikhail Mishustin is the first senior politician here to fall sick with coronavirus.
He looked exhausted as he informed President Putin, via a video call, that he had tested positive and was handing over his responsibilities and heading into self-isolation.
Mr Putin said it only showed how the virus did not discriminate. He told the prime minister to give him a call when he got to hospital.
Mr Mishustin himself used the chance to urge all Russians to take coronavirus seriously, and to stay at home as an 11-day, extended May holiday begins.
Officials fear warmer weather will send families rushing to the countryside as usual. So Moscow is increasing the number of police patrols in the coming days, to ensure people stick to the strict lockdown.
Despite the sharp rise in cases, the Moscow-based coronavirus headquarters says 1,073 people in Russia have now died of coronavirus, a relatively low number for Russia's size.
Presidential spokesman Dmitry Peskov says Russia's reaction to the pandemic has enabled it to avoid an "Italian scenario".
But President Putin warned this week that Russia did not have enough protective equipment for health workers and medics have complained in several regions of having insufficient protective suits.
Moscow's Mayor, Sergei Sobyanin, has meanwhile said he believes many of those living in the Russian capital do not realise how serious the situation is.
He said he had seen more people violating the restrictions, estimating his city was only a quarter of the way through the crisis.
"If we see things are getting better, then of course we will reduce the restrictions. But until that happens, you need to be courageous and patient. It's very important for you and your health," he said.