Beamon suffered the injury during the team's loss to Quinnipiac last week and missed the Jaspers' overtime win over Marist on Sunday.
The 6-foot-4 senior swingman is currently 33rd in the country in scoring, averaging 20.1 points per game. He is also the team's leading rebounder (6.6 per game). The Jaspers (12-3, 5-1) are tied with Iona and Canisius atop the Metro Atlantic Athletic Conference.
"George is going to be evaluated on a day-to-day [basis]," coach Steve Masiello said Tuesday. "There's a chance he could play Thursday [against Siena]. ... I'm gonna be extremely cautious with him after what we went through last year."
Beamon, an All-MAAC first-teamer as a sophomore two years ago, played in just four games last season due to a severe ankle injury.
Manhattan is seeking its seventh bid to the NCAA tournament but first since 2004. The Jaspers are projected as a No. 13 seed in the latest edition of ESPN.com's Bracketology.