The Rev. Joseph Anselmo Mwagambwa told CNN the attack occurred Friday as he left an Internet cafe in Zanzibar City. He was transferred to a hospital in Dar-es-Salaam on the mainland.
Last month, Katie Gee and Kirstie Trup, both 18, were attacked in Stone Town, the historic central section of Zanzibar City. The British nationals were in Zanzibar as volunteer teachers.
In July, a businessman of Arab descent was also sprayed with acid.
The New York Times said that two Catholic priests have been shot in the past year. One was wounded last year and the other killed in February.
Catholic churches have also been set on fire.
Zanzibar, about 22 miles from the Tanzanian mainland at the closest point, is semi-autonomous and predominantly Muslim. The mainland is split more or less evenly between Muslims, Christians and those who practice indigenous faiths.