The attack happened around 10:30 a.m. at the St. Polycarp Catholic church in Nairobi and was immediately blamed on Somalia's al-Shabaab Islamist militants, the BBC reported.
Nairobi Police Chief Moses Ombati told the Sunday Nation newspaper some of the injuries were caused by a panic stampede after the blast.
He said no one saw the person who threw the grenade, but three people were arrested while taking pictures of the blast scene. The three told police they were Somali television journalists, the newspaper said.
Soon after the explosion, a group of youths began attacking a nearby mosque, but they were dispersed without incident by police, Ombati said.
Al-Shabaab militants have targeted Kenyan churches in the past in retaliation for Kenya's participation in an African Union military mission in Somalia to roust the group considered to be a terrorist organization.