The school announced Hare had taken the leave of absence Friday.
The 6-foot-10 Hare averaged 5.2 points and 4.0 rebounds while starting 19 games as a freshman last season and was expected to be a key piece for the Rams this season.
However, sources told ESPN.com that there is a chance that Hare -- who will remain enrolled as a student at the school -- will not return to the team.
Rhode Island finished 8-21 last season in Dan Hurley's first at the helm. However, the Rams are expected to take a step forward with the addition of transfers Gil Biruta (Rutgers), Biggie Minnis (Texas Tech) and Jarelle Reischel (Rice).
The loss of Hare will certainly have an impact on URI this season as Hurley was hoping that the Saginaw, Mich., native would develop into one of the top frontline players in the A-10.