The officer bit into his sandwich and felt a odd texture and heard a crunching sound, police officials said. "He then noticed glass in his sandwich".
The officer was taken to Grant Medical Center at about 3 p.m. where he was held overnight. When the officer checked his mouth, he realized he was bleeding.
Detectives said it's not clear whether the incident was accidental or intentional.
Columbus Public Health officials say they plan to visit the restaurant Tuesday to help determine what happened.
No charges have been filed.
The officer's identity and the restaurant's name are being withheld as Columbus police investigate. Five officers were killed in Dallas on July 7 and three were killed in Baton Rouge last weekend.