The eggs were in a nest in a cooling tower at the partially decommissioned Bradwell power station in Southminster, Essex.
Peregrines are protected by law and it is a criminal offence to take or destroy their eggs.
Essex Police said it was not yet known whether the damage was caused by another bird or by humans.
Power station owner Magnox had recently been granted a licence by Natural England to relocate the eggs to a foster bird elsewhere.
But before that could happen the eggs were smashed.
Magnox is working with Essex Police to establish what happened.
The company has also placed nest boxes at the site to help give the peregrines a more suitable location to breed.
Police are investigating after peregrine eggs were found smashed in a nuclear power station.