Packers head Coach Mike McCarthy said decisions would soon be made on whether to place the pair on injured reserve, which would rule them out for the rest of the season.
McCarthy said Finley hurt his knee in the first quarter of Sunday's loss to Washington and underwent successful surgery Tuesday, while Barnett suffered a wrist injury Oct. 3 against Detroit and went under the knife Wednesday.
Another injured Packer, quarterback Aaron Rodgers, didn't practice Wednesday after suffering a concussion in the Washington game. McCarthy said he won't know more about the signal-caller's status until testing is completed on Thursday morning.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys