The attack took place mid-morning at St. Polycarp’s church in the Kenya capital, Nairobi.
A police spokesman blamed sympathisers of Somalia's al-Shabab Islamist militant group, the BBC reported.
Nairobi and the port city of Mombasa have suffered a series of grenade attacks since Kenya sent troops into Somalia last October, the BBC noted.
In July there were gun and grenade raids on two churches in Garissa, killing at least 17 people.
The numbers of those wounded in Sunday’s attack have not been confirmed, but according to CNN, the Kenya Red Cross said that six children were taken to hospital. Other reports said that as many as nine children were injured.
The attack follows another recent one in the African continent, when the previous Sunday a suicide bomber attacked St. John's Cathedral in Bauchi, in northern Nigeria, causing two deaths and many injured.