Claiborne had an MRI on Friday after sitting out of the afternoon practice. He said he suffered the injury on Wednesday but hoped to be able to continue to practice.
He spent Saturday's morning walkthrough next to secondary coach Jerome Henderson to soak up more of the defense.
"A little bit disappointing," Claiborne said, "but it's not too much because I know it's not something serious. I know it's something I can come back from. You can't just get mad over something you can't control."
The Cowboys had been force-feeding Claiborne the defense after he missed the entire offseason recovering from left wrist surgery before the NFL draft. Claiborne worked with the No. 1 defense since camp opened and has been replaced by Orlando Scandrick.
"It's me just being angry because I missed a lot of reps in the past, and I wish I could have those reps back," Claiborne said.
While the Cowboys are relieved the injury is not serious, they know Claiborne cannot miss much time on the field.
"Obviously when you're not learning on the field it's a setback and he's got two fantastic coaches with Jerome Henderson and Joe Baker," defensive coordinator Rob Ryan said. "He'll be with them and he'll get to know them really well and they got to stay up with him. You can't replace a rep on the field and that's going to be tough for him. It's a tough transition anytime you're a rookie, he's a damn good young man and I'm sure he'll caught up to speed as fast as he can."
Elsewhere on the injury front, running back Phillip Tanner will return to Dallas on Monday to have surgery on his right hand. He will miss the Aug. 13 preseason opener at Oakland, but coach Jason Garrett said Tanner could return in one to two weeks.
Hall of Fame running back Emmitt Smith had a similar injury in the mid '90s and did not miss a game. When Tanner, who backs up DeMarco Murray and Felix Jones, returns he will be fitted with a special glove for extra protection.
Wide receiver Danny Coale and guard Mackenzy Bernadeau have been cleared off the physically unable to perform list and will be in pads for the first time on Tuesday. Per league rules, players have to go through a three-day acclimation period before donning pads.
Bernadeau did not take a snap in the offseason because of hip and knee surgeries after joining the Cowboys as a free agent with a four-year, $11 million deal from Carolina. Coale, the team's fifth-round pick, has been out since mid-May because of a stress fracture in his foot.
Defensive end Jason Hatcher was to miss practice Saturday because of a strained hamstring, but the team does not believe the injury is serious.