The attacker targeted the Sunday school section of St Polycarp’s church on Juja Road.
The Daily Nation newspaper said one child was killed.
A spokesman for the police said they suspected sympathisers of Somalia’s al-Shabab Islamist militants were to blame for the attack.
The spokesman, Charles Owino, told Reuters news agency: “There was an attack at St Polycarp’s church on Juja Road. Three children were injured.”
The Daily Nation quoted local police as saying that a number of those hurt at the church were injured in a stampede after the attack.
Mr Owino added: “We suspect this blast might have been carried out by sympathisers of al-Shabab. These are the kicks of a dying horse since, of late, Kenyan police have arrested several suspects in connection with grenades.”
Kenyan troops are at present part of an African Union force that has forced al-Shabab from its last Somali urban stronghold of Kismayo.
Nairobi and the port city of Mombasa have suffered a series of grenade attacks since Kenya sent troops into Somalia last October.
The attacks in Mombasa escalated after radical Islamist preacher Aboud Rogo Mohammed was killed in a drive-by shooting in August.
In July, 15 people were killed in raids on churches in Garissa, near Kenya’s border with Somalia.
There was speculation that al-Shabab or its sympathisers were responsible.
Those attacks prompted the country’s Inter-Religious Council chairman to urge a united front against sectarian division.
Adan Wachu told the BBC Network Africa programme at the time: “There are people out there who are determined to make Kenya another Nigeria.
“It’s not going to be allowed to have a sectarian division in this country – whoever wants to do that will of course fail.”
Attacks on churches in Nigeria have been frequent this year.
Many of them have been blamed on the Boko Haram group, which wants to establish Islamic law in a country where the north is largely Muslim and the south mainly Christian and animist.