Police say they believe Sunday’s blast was caused by a bomb, and that a suspect has been arrested.
The explosion occurred at the official opening of the new Roman Catholic church in the suburb of Olasiti.
The Vatican’s ambassador to Tanzania and the archbishop of Arusha were attending, but were not hurt.
The attack happened despite heavy security presence in the area.
Police say a woman was killed but a local priest, Father Peddy, said three people had died on their way to hospital.
“I never expected anything like this to happen because this is not a city – it’s a village,” he told the BBC.
Tanzanian Foreign Minister Bernard Membe said in a Twitter message he was “greatly shocked” by the attack.
Tanzania has seen a rise in sectarian violence between Christians and Muslims in recent times.
Last month, police in southern Tanzania used teargas to disperse about 200 Christian rioters attempting to torch a mosque over an animal slaughtering conflict.
In February, a Catholic priest was shot in the head on the largely Muslim island of Zanzibar.