A child was killed and more than 30 people were injured in the blast in a suburb of the northern Tanzania city of Arusha.
The parishioners had been waiting for Bishop Josaphat Louis Lebulu of the Arusha Diocese to arrive along with the unidentified Vatican representative, China's Xinhua news agency said.
"We were trying to organize ourselves for the mass, when we heard loud sound, the situation that made more people to start rushing out of the church," a witness told Xinhua.
Police announced they had arrested a suspect in the bombing with the assistance of witnesses at the scene.
The incident marked the first time a church in Arusha had ever been attacked, Xinhua said.
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