The Browns also placed CB Ifo Ekpre-Olomu, TE Randall Telfer, and RB Glenn Winston on the reserve/non-football injury list.
Players placed on reserve/NFI list are eligible to return to practice anytime between Week 6-11.
Shaw, 23, signed on with the Browns as an undrafted out of South Carolina last year. He has two years remaining on his three-year, $1.53 million contract, which includes a base salary of $525,000 for the 2016 season.
In 2014, Shaw wound up appearing in one game and completing 14 of 28 attempts for 177 yards, no touchdowns and an interception.
Ekpre-Olomu, 22, sustained a torn ACL a while back, so this news shouldn’t come as a big surprise. His knee injury was one of the reason that he nearly dropped out of the draft completely.
The Browns wound up using a seventh-round pick on Ifo Ekpre-Olomu a few months ago.
During his four-year career at Oregon, Ekpre-Olomu recorded 244 tackles, 6.5 sacks, nine interceptions, and eight forced fumbles.