The president is on his way to Ohio to speak about economic prosperity, visit a Whirlpool plant, and attend a fundraising reception.
Mr DeWine has no symptoms and has returned to Columbus where he will quarantine for 14 days.
The Covid-19 test was administered as part of the standard protocol when meeting with the president.
Both the governor and first lady, Fran DeWine, who also has no symptoms, will be tested at home.
Ohio's lieutenant governor John Husted also took a test today which was negative.
— Governor Mike DeWine (@GovMikeDeWine)August 6, 2020