A man has been arrested after a woman, baby and pastor were shot inside a church in the US state of Alabama.

Dallas County District Attorney Michael Jackson told the Associated Press suspect James Minter was arrested after the Sunday shooting at the Oasis Church in East Selma.

Mr Jackson said it is believed the shooting is a domestic-related incident and that the shooting was not motivated by race.

The suspect, James Minter, was arrested after the shooting. (AAP)