Garissa is an important military base from where ground forces have been deployed into Somalia to fight al Qaeda-linked insurgents.
Kenya has been struck by a series of blasts since it sent troops across the border in October to try to crush the al Shabaab militants. The capital and other parts of Kenya have suffered a string of grenade attacks.
"The goons were clad in balaclavas and hurled the grenades at the Catholic Church and the AIC (African Inland Church) in the town," regional deputy police chief Philip Ndolo told Reuters.
"So far we have at least 10 killed, and more than 40 wounded following the grenade attacks," he said.
A blast hit a night club in the port of Mombasa last Sunday, killing one man, a day after the US embassy in the East African country warned of an imminent attack on the city.
Garissa is situated about 100kmfrom Kenya's Dadaab refugee camp, where gunmen kidnapped four aid workers and killed a driver on Friday.
It was the first kidnapping of foreigners since Kenya deployed the troops. –