A gardener found the peacock's body on Tuesday on the lawns of the premier's house where the birds wander freely, a police official said.
He said the incident was reported to Superintendent of Police Arshad who summoned the constables deployed in the house.
Initially, Arshad denied the incident, saying some officials had been penalised for not being present for duty at the time.
One of the suspended constables, however, told The Express Tribune that 21 constables were summoned by the SP on Wednesday.
A gardener found the peacock's body on Tuesday
"He said the constables said they were on duty but did not anticipate a cat eating the peacock at night," according to the report.
The SP cleared 18 security personnel as they were not manning the lawn but issued formal orders of suspension for the remaining three police constables, who were on guard near the lawn where the bird was attacked, the paper said.
Sharif's farm house is located in Raiwind area.