Ravi Yadav (1) and Deepu Tripathi (9 months), died within half-an-hour of being given the vaccine at a public health centre in the village, about 47 kms from here, they said.
An inquiry would be conducted under the supervision of the Additional District Magistrate, Satna.
The injections used for administering the vaccine have been seized and sent for testing, they added.
Officer-in-charge of the health centre, Dr D N Gautam, said the inoculation officer, Satyendra Singh, had been placed under immediate suspension after the incident.