USA Today reported the first-round pick could miss up to a week.
Claiborne was pulled from practice Friday and could only watch the team's walkthrough practice in Oxnard, Calif., on Saturday.
"I can't control this, so I'm not going to beat myself up over it," he said. "All I can do is go in there and do what I need to do with rehab."
Cowboys coach Jason Garrett said Claiborne initially injured the knee on Wednesday and practiced through it. He received treatment on Thursday and practiced Friday afternoon before the knee flared up.
Claiborne was the sixth overall pick after a standout career at LSU. He also missed minicamp because of wrist surgery in the spring but attended defensive meetings.
Defensive coordinator Rob Ryan said Claiborne has picked up the Dallas defense quickly, despite being slowed by the injuries.
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