That thrusts Bailey Zappe, a fourth-round pick out of Western Kentucky, into the No. 2 spot behind Jones.
Zappe is projected to start in Sunday's home game against the Detroit Lions if Jones -- who has been limited in practices on Wednesday and Thursday -- isn't cleared to return.
"If that's what happens, that happens. That's a question for Coach Belichick. I'm not going to get into those details," Zappe said.
The Patriots also signed 31-year-old quarterback Garrett Gilbert to their practice squad Wednesday, and in a reflection of the team's unsettled picture at the position, he was swarmed by reporters in the locker room Thursday.
Gilbert likes what he has seen from Zappe in recent days.
"I've been very impressed," he said. "I've spent a good amount of time with him in extra meetings, and being a young guy thrust into this position he's done a very good job with it the first couple days. He's got good command of the offense. He's been willing to ask questions and learn as we continue to prepare for Sunday."
Starting in place of Jones on Sunday, Hoyer suffered the concussion on a first-quarter sack in a 27-24 overtime loss to the Green Bay Packers, which put Zappe into the game. He finished 10-of-15 for 99 yards with one touchdown and was sacked three times.
Hoyer, who turns 37 on Oct. 13, will miss at least four games by going on IR.