Siemian was placed on season-ending injured reserve. Joseph said he will not require surgery and the plan is for rest and rehabilitation.
Siemian was injured during Thursday night's 25-13 victory over the Indianapolis Colts. He was sacked in the first quarter by Colts linebacker Barkevious Mingo and landed on his shoulder.
The injured shoulder is the same one that Siemian had surgically repaired after last season.
Siemian passed for 2,285 yards and 12 touchdowns this season while being intercepted 14 times.
Brock Osweiler replaced Siemian against the Colts and accounted for three touchdowns (two passing, one rushing).