Elderly priest Joseph Mwand'amba was attacked after leaving an Internet café in the Mlandege area. "He sustained burns in his face and shoulders. The acid burnt through his shirt," Zanzibar police spokesman Mohamed Mhina said.
Tensions have risen between the majority Muslim population and Christians have been on the increase in recent years, as well as on mainland Tanzania.
It's the fifth such incident in a series of assaults on religious figures in the country since Novenber, when a Muslim cleric was hospitalized with acid burns. A Catholic priest was shot dead in February.
An attack on two British girls in August occurred in the same part of Stone Town. The teenagers, Katie Gee and Kirstie Trup had acid flung at them as they visited Zanzibar on a volunteering holiday. Doctors believed that their attackers used sulfuric acid from a car battery. It's believed that the girls will need skin grafts.