Fr Ambrose Mkenda was shot by two men on a motorcycle in an area called Tomondo as he got out of his car.
He was returning home after celebrating Mass.
Following the attack Christians in the island have demanded better protection and have accused the police of inaction.
This is the first time such an attack has occurred in the Island, which in recent months has witnessed violent protests linked to Uamsho, an extremist Islamic group whose name means "Awakening" in Swahili.