“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 is 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.
An AFP reporter said that several wounded people were taken to hospital, and that police had closed off roads around the church.
Tensions have been high between Tanzania’s Christian and Muslim communities in recent months, although there was no indication of what had caused Sunday’s explosion.
In February, a Catholic priest was shot dead outside his church on the largely Muslim archipelago of Zanzibar, the second such killing in recent months. A church was also set on fire on Zanzibar in February.
Last month, in the far south of Tanzania, police fired tear gas to disperse around 200 Christians rioters attempting to torch a mosque over an argument over who should be allowed to slaughter animals.
Tanzanian foreign minister Bernard Membe said in a message on Twitter that he was “greatly shocked” at the news of the blast.
