Officials said the incident was reported at about 5 PM. During the X-ray scanning of the bag belonging to P Kumar, CISF personnel found five .32 calibre bullets in it.
Kumar had come with his family for a visit to the historical monument.
"He was later handed over to Delhi Police as carrying arms and ammunition is prohibited in the premises of the Red Fort. The man said he works as a private body guard," a senior official said.
The Central Industrial Security Force is tasked with securing the Red Fort.