At least 30 people were injured, three seriously, in a suspected bomb attack Sunday at a packed new Catholic church in the northern Tanzanian city of Arusha, police said.
Witnesses said at least one person had been trampled to death in the stampede after the blast.
The Vatican's ambassador to Tanzania, Archbishop Francisco Montecillo Padilla, was attending mass at the church but was not harmed, officials said.
"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.
However, tensions have been high between Tanzania's Christian and Muslim communities in recent months, and local member of parliament Godbless Lema condemned the blast as the work of "criminals".
"Religious fundamentalism is a reality in this country, but the government does nothing," he said angrily outside the church, as police cordoned off the area and ordered people away from the building.
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.
The newly built church, in the Olasti district on the outskirts of Arusha town, was celebrating its first ever mass when the blast took place, and people were squeezed into the church building as well as sitting on benches outside.
"When it exploded there was a stampede, people running in all directions, walking on each other, children were screaming and women crying," said Viviana, who was helped out of the church by her son.
"I saw a dead woman trampled, I think even her two children were killed in the same way," said a woman, who gave her name only as Mariana.
An AFP reporter said that several wounded people were taken to hospital, and that police had closed off roads around the church.
Worshippers angrily accused the police and the government of failing to properly protect them.
"There were so many people, the church was full, and the faithful were sitting on benches outside - it was a great day of celebration," said Jacob, a motorcycle taxi driver, who had been at the mass.
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 Christian 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.