Bryant had arthroscopic surgery to repair a torn meniscus in his left knee on Tuesday. Clayton missed more practice time with a sore hamstring that will keep him out of Saturday's game at Tennessee.
Coach Raheem Morris said Bryant, who led Tampa Bay with 83 receptions for 1,248 yards and seven touchdowns in 2008, will sit out at least three weeks and be ready to play in the Sept. 13 regular-season opener against the Dallas Cowboys.
"Probably could be back for the fourth [preseason] game. Don't know. You might want to get a little test run to see what he can do," Morris said.
Running back Derrick Ward returned to practice after missing several days with a foot sprain. Offensive tackle Jeremy Trueblood (back) practiced in the evening, but linebacker Geno Hayes was held out of both of Tuesday's workouts with a mild hamstring strain.
"He made all the kicks today, and he kind of strained it a little bit, so he stepped out," Morris said.
Bryant called the injury "frustrating," though not serious.
"It's nothing big," the kicker said. "But it's not an overnight thing."
Morris wouldn't speculate on what it might mean to Bryant's chances of retaining the kicking job.
"We've just got to get him healthy, get him to the games so he can go out there and compete," Morris said. "Usually you don't have two guys. Usually you've got to get somebody off the street right now to come compete with him. So, we as an organization are kind of in a fortunate situation. But you still want to see Matt Bryant at his very best to let him go compete."