DeWine said he tested positive during normal testing protocol required to meet President Donald Trump, who traveled to Ohio Thursday to visit a manufacturing plant and attend a fundraiser in northern Ohio.
DeWine, 73, tweeted that he's experienced no symptoms but will self-quarantine with his wife at their Cedarville, Ohio, home. Lt. Gov. Jon Husted has tested negative.
The Republican governor's positive test prevented him from greeting Trump Thursday on the tarmac at Burke Lakefront Airport in Cleveland, and barred him from attending the later fundraiser.
DeWine has asthma and has taken medication through inhalers since he was in his mid-20s.
DeWine has received praise from members of both parties, partly for imposing a statewide mask order early. Cases, however, have recently climbed across Ohio, as they have in other states. He'd allowed some businesses to reopen in May and recently ordered alcohol sales at bars and restaurants to end at 10 p.m., following reports that customers were not complying with distancing measures.
"We are saddened to hear of Gov. Mike DeWine's test result," Ohio Democratic Party Chairman David Pepper said. "We know how hard he's been working to keep Ohioans safe, and this is just one more reminder that this virus can impact everyone."
DeWine, who took office in January, is the governor of a key battleground state for the 2020 presidential election. Thursday's visit and fundraiser is part of the Trump campaign's effort to appeal to voters in the state, which has a large manufacturing sector.