Osuna, 23, has agreed not to appeal the suspension, which is retroactive to May 8 and extends through Aug. 4. He will wind up missing 89 days, which would cost him about $2.54 million of his $5.3 million salary.
Osuna was arrested by Toronto police on May 8 and charged with assaulting a woman. He was then placed on administrative leave and the league has been investigating the charges since.
In a statement, the Blue Jays said they supported MLB's decision to suspend Osuna and that they would have no further comment, citing the legal matters involved.
"I don't have much of a reaction other than you take what MLB does and trust that and live with that and let it go through its course,'' Blue Jays manager John Gibbons said before Friday night's road game against the Los Angeles Angels. "We knew something was coming down. Actually, it took a while. Hopefully, it all gets worked out on both sides and everyone gets the help they need and everything works out fine.''
Osuna has a Toronto court date on July 9 and will plead not guilty to the charges, according to his attorney, Domenic Basile.
Asked if it was better the Blue Jays now knew the length of the penalty, Gibbons said: "I guess that helps."
"We've kind of moved past that anyway and made do with what we've had," he said.
Osuna has appeared in 15 games this season with nine saves and a 2.93 ERA. The righty was an All-Star last year when he went 3-4 with 39 saves and a 3.38 ERA.
MLB and the players' union agreed on a domestic violence policy in 2015. It allows the league to discipline a player for a domestic violence incident regardless of whether there are charges or a trial.
Osuna is expected to participate in a confidential and comprehensive evaluation and treatment program supervised by the joint policy board of MLB and the players' association.
Pitcher Aroldis Chapman was the first player disciplined under the policy when the league suspended him for the first 30 games of the 2016 season. Days later, shortstop Jose Reyes was suspended 51 games.
The Associated Press contributed to this report.