The Ohio State product suffered a torn pectoral muscle while bench-pressing at the NFL Scouting Combine.
Price getting cleared was expected after the center noted this spring he was "way ahead of schedule" in rehab. Being given the go-ahead before training camp in July keeps the No. 21 overall pick on track for Week 1.
Cincinnati's offensive struggles the past few seasons stemmed in part from problems along the line. The Bengals significantly upgraded the blocking unit this offseason by adding Price and left tackle Cordy Glenn. The 6-foot-4, 305-pound Price entered the draft as one of the most pro-ready blockers and projects as the opening-day starter at the pivot.