Unidentified assailants hurled Molotov cocktails at the Sidi Ahmed Ouerfelli mausoleum in the Sousse town of Akouda.
Tunisia's Sufi community denounced the desecration of the 35th shrine in just seven months.
"The people behind all the attacks are Wahhabis," AFP quoted a Sufi union official as saying at a Tunis press conference.
"This is just the beginning," Mazen Sherif said. "They will go on to destroy the sites in Carthage, El Jem and Duga. Then they will force men to grow beards and women to wear the hijab," he said.