Miller was hurt throwing a short pass in practice but was not hit on the play. There was no indication from the university when the surgery would take place.
"My thoughts and prayers are with Braxton and his family," Ohio State coach Urban Meyer said. "This is an unfortunate injury to a young man who means so much to this program and to Buckeye nation."
The senior's throwing shoulder was surgically repaired in February after he was injured during the Orange Bowl loss to Clemson in January.
Miller had been nursing the shoulder along during preseason camp. He did not participate in contact drills during the spring after the surgery.
Miller indicated through the university that he plans to remain in school and return next season. He is eligible for a redshirt.
"I love Ohio State and Buckeye nation, and my goal is to come back from this injury stronger and better than ever," Miller said. "I am on course to graduate in December and I want to attend graduate school and then return to lead the Buckeyes next season.
"In the meantime, I want to give all the support I can to my coaches and teammates as they chase a championship this season."
The Buckeyes returned to practice Tuesday morning without Miller. Redshirt freshman J.T. Barrett likely will be the starting quarterback for the season opener on Aug. 30 against Navy. Barrett and third-year sophomore Cardale Jones were competing for the backup job before Miller went down.
Jones is the lone quarterback on the Buckeyes' roster with game experience. He took 39 snaps in wins over Florida A&M, Penn State and Purdue last season.
Ohio State is ranked No. 5 in the preseason Associated Press poll and was considered a contender to land one of the berths in the four-team playoff to determine a national champion this season. But the loss of Miller caused Ohio State's odds in Las Vegas for winning the title to plummet from 10-1 to 40-1.
Last season, Miller completed 63.5 percent of his passes for 24 touchdowns and seven interceptions and also ran for 1,068 yards and 12 touchdowns. He is a two-time Big Ten offensive player of the year.