It was the second time Stafford hurt the shoulder this season. He was also injured in the season opener, and Hill started the next five games before hurting his non-throwing arm against the Giants.
Stanton started one game last season.
MLive.com reported Tuesday that preliminary tests revealed Stafford has a Grade 3 separation of his throwing shoulder, meaning he would be lost for the season.
Stafford is expected to get a second opinion from Dr. James Andrews, just as Stafford did earlier this season for a previous shoulder injury. MLive.com reported that no decisions about Stafford's status for the rest of the season have been made yet.
The Lions also added another quarterback when they claimed rookie Zac Robinson off waivers from Seattle.
The Associated Press contributed to this report.