The wide receiver has undergone surgery to correct the problem, and is expected to miss around six weeks while recovering from the procedure.
Head coach Mike Smith told the team's official website: "Drew felt some discomfort in his foot at the end of minicamp.
"We decided to send him to the doctors for some evaluations and it was determined he had suffered an injury that would require a procedure.
"He recently had the procedure done and we expect him to miss around six weeks, which is why we have decided to place him on Training Camp PUP."
Davis recorded 256 receiving yards and scored two touchdowns for the NFC South side last season.