"There have been 30 people wounded, three in a serious condition, and one person has been arrested," said regional police chief Liberatus Sabas.
It was not immediately clear what caused the explosion.
"This a sad day, our security forces are mobilised, and the culprits will be arrested and brought to justice," said Arusha's commissioner Magesa Mulongo.
"For the time being we don't know if it is a bomb," he added.
The blast took place outside a Roman Catholic church in Arusha, a town popular with tourists visiting the nearby Serengeti national park and snowcapped Mount Kilimanjaro.