The rookie out of Memphis went to the trainers table, and then exited the field, not long after missing a 34-yard field goal attempt wide right.
Elliott made a saving tackle on Ryan Switzer's 61-yard return on the opening kickoff.
The 22-year-old Elliott was signed off the Bengals' practice squad in September after Caleb Sturgis was lost to a hip flexor injury. He has connected on 17-of-21 field goal attempts, including five from 50-plus yards.
Reserve linebacker Kamu Grugier-Hill was practicing field goal tries along the sideline shortly after Elliott exited. One kick missed the net and went into the stands.