A teenager from the Dayton area of the state was also awarded a college scholarship offered by the program.
The winners were selected in a random drawing and had their information confirmed before the formal announcement at the end of the Ohio Lottery's Cash Explosion TV show.
Abbigail Bugenske, of Silverton near Cincinnati, was the one million dollar winner, while Joseph Costello, of Englewood near Dayton, won the college scholarship.
"We're excited that this has inspired so many Ohioans to get vaccinated, and we're thrilled to announce the winners of the first round of drawings," said governor Mike DeWine.
More than 2.7 million adults signed up for the $US1 million prize and over 104,000 children aged 12 to 17 entered the draw for the college scholarship, which includes tuition, room and board, and books.
Four more million dollar and college scholarship winners will be announced each Wednesday for the next four weeks.
DeWine, a Republican, announced the program on May 12 to boost lagging vaccination rates.
The Ohio Lottery conducted the first drawing on Monday afternoon at its draw studio in Cleveland using a random number generator to pick the winners ahead of time, and then confirmed the eligibility of the ultimate winner.
The names of entrants who do not win will be carried over week to week. The deadline for new registrations is just before midnight on Sunday.
"I know that some may say, 'DeWine, you're crazy! This million-dollar drawing idea of yours is a waste of money'," the governor said when he announced the incentive. But he said that with the vaccine now readily available, the real waste "is a life lost to Covid-19''.
The number of people in Ohio aged 16 and older who received their initial Covid-19 vaccine jumped 33 per cent in the week after the state announced its million-dollar incentive lottery, according to an Associated Press analysis. But the same review also found that vaccination rates are still well below figures from earlier in April and March.
More than 5.2 million people in Ohio had at least started the vaccination process as of Monday, or about 45 per cent of the state.
About 4.6 million people are done getting vaccinated, or 39 per cent of the state. Nationally, more than 165 million Americans have started the vaccination process, or nearly 50 per cent of the population. More than 131 million are fully vaccinated, or nearly 40 per cent.
DeWine's proposal inspired similar vaccine-incentive lotteries in Colorado, Maryland, New York state and Oregon.