The Fort Worth Star-Telegram earlier reported Pachall's surgery.
Pachall injured his left arm at the end of a second-quarter running play Saturday against Southeastern Louisiana.
With Pachall out, Trevone Boykin will make his first start of the season at quarterback Thursday when the Horned Frogs travel to Texas Tech.
Boykin played the final nine games in 2012 after Pachall was arrested and went into a substance-abuse program.
Pachall returned in the spring, and the quarterbacks split time in last week's opener against LSU. They were both on the field for the first play, with Pachall under center and Boykin at receiver.
Boykin had the first three catches of his career before Pachall appeared to get get his arm caught under two defenders as he was tackled near the sideline.
After Pachall's injury, Boykin led TCU on three consecutive scoring drives to help the Frogs pull away from Southeastern Louisiana, 38-17.