In addition, the 20-year-old Barrett must complete a three-day alcohol education program as a result of the misdemeanor stemming from his stop at a DUI checkpoint early on Halloween.
Barrett must complete the class and pay the fine by Feb. 15 or face jail time, Judge H. William Pollitt said as he accepted Barrett's plea.
"I'm just truly sorry," Barrett said in a brief statement.
An additional charge of backing without safety was dismissed, and the case has been closed.
Barrett was home Oct. 31 relaxing with friends when a "heavily intoxicated" friend stopped by and Barrett decided to drive him home, said Barrett's attorney, Phil Templeton, who wouldn't identify the friend.
The lawyer noted to the judge that Barrett's blood-alcohol level of 0.099 was only slightly above the legal limit of 0.08 for adults, though he acknowledged Barrett was underage. In Ohio, the limit is 0.02 for people under 21.
On the field, Barrett's situation for Ohio State has also been resolved, as he is in line to return to the starting lineup for the No. 3 Buckeyes against Illinois on Saturday.
The redshirt sophomore was suspended one game by coach Urban Meyer and lost his summer financial aid in 2016 as a result of the OVI, and Barrett watched the Buckeyes' 28-14 win over Minnesota last week from the press box. Cardale Jones started in his place.
"I think [he handled it] well," Meyer said Monday. "It's a mistake made -- a serious mistake -- by a kid that's really lived most of his life mistake-free. He's a kid that's human, and I still have these conversations with him.
"You can handle when people say you're not very tall or fast enough or you don't throw far enough, but when someone challenges who you are as a person or a man, that's tough. He's probably not had that happen to him very often."
The Associated Press contributed to this report.