"The baby was identified as Bharat Sharma, son of Divendra Sharma - a resident of Begamganj colony under city's Mahakal police station area," sub-inspector Rohit Yadav said.
The baby was vaccinated last night and his family has lodged a complaint, he said.
Family members alleged that the baby died to due to the Pentavalent vaccine, police said.
The body was sent for postmortem to ascertain the cause of his death.
The syringe and other stuff used during the procedure were also sent for test, he added.