A statewide alert was sounded in Madhya Pradesh after the blasts in Bodh Gaya on Sunday.
Security was upgraded at Buddhist sites including Sanchi as a precautionary measure.
The Police Headquarters ( PHQ) has issued the alert.
Additional director general of police (ADG), Intelligence, Vivek Johri, said the directives have been sent to all the districts.
He said security had been beefed up at Sanchi and the other Buddhist sites.
The police official said in view of the possibility that the blasts may have been a reaction to the attacks on Muslims in neighbouring Myanmar; the police here are also on the alert and have increased surveillance at the Buddhist temples in MP.
The stupa at Sanchi is a world heritage site. The series of blasts that rocked the Mahabodhi Temple in Gaya (Bihar) injured two persons.
MAHAKALESHWAR TEMPLE PUT ON ALERT
Security has been beefed up at the world famous Mahakaleshwar Temple in Ujjain in the wake of serial blasts in Bodh Gaya.
The police have sounded an alert at religious places following the blast.
Ujjain superintendent of police Anurag said heavy police force was deployed at the temple that draws thousands of devotees every day. “Additional security, including anti-sabotage team, has been positioned at the temple and its surrounding areas,” he said.