An MRI exam taken Wednesday revealed the tear, which will require surgery. He hurt the knee in practice on Tuesday.
Weaver transferred to Syracuse after Hofstra eliminated its football program following the 2009 season.
He caught six passes for 88 yards in Syracuse's first two games, and scored the first touchdown of the year for the Orange (1-1) on a 23-yard catch over the middle from quarterback Ryan Nassib in a 29-3 victory at Akron.
Weaver, a fifth-year senior, played three seasons at Hofstra and caught 135 passes for 1,416 yards and eight touchdowns.