Delta state police spokesman Andrew Aniakama said St Paul Catholic Church in Adagbrasa collapsed midway through the service.
Church collapses are relatively common in Nigeria. In December 2016 dozens of worshippers were killed when a church collapsed in Akwa Ibom state.
The Nigeria Society of Engineers has blamed the problem mainly on the use of substandard materials and violations of building regulations.
The governor's spokesman, Charles Aniagwu, said the government has dispatched a team to determine the cause of Sunday's collapse.
Nigeria's Senate president Bukola Saraki said the government will provide assistance "to see that survivors are rescued and treated".
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