Toronto Police would not release further details regarding the alleged incident.
Osuna was released from custody and has a court date on June 18 in Old City Hall Court. The 23-year-old has a 2.93 ERA in 15 appearances this year for the Blue Jays. He was selected for his first All-Star team in 2017, after posting a 3.38 ERA and 39 saves, while leading Major League Baseball with 58 games finished.
The right-hander from Juan Jose Rios, Mexico, is making $5.3 million this season.
His arrest comes two days before the Blue Jays plan to give away 15,000 Roberto Osuna t-shirts prior to a game against the Seattle Mariners Thursday at Rogers Centre in Toronto.
MLB officials have not yet commented on the arrest or potential discipline from the league.
Osuna allowed one hit and had a strikeout in one shutout inning against the Tampa Bay Rays in a Blue Jays victory Sunday at Tropicana Field in Tampa, Fla. He earned his ninth save of the season for his effort.