The imam had just finished leading the night prayer when Israeli police attempted to disperse worshippers by force, leaving many injured, some seriously, Palestinian Red Crescent said.
Sabri was taken to the Al Maqassid Hospital in eastern Jerusalem and his condition has not been disclosed.
The shooting occurred just hours after Rafaat al-Herbawi, 30, was killed during protests at the mosque as tensions rise across the illegally occupied West Bank after Israel installed metal detectors at the entrance to Al-Aqsa following a shootout on Friday left five people dead.
More than 300 Palestinians have been killed in alleged attacks on Israelis or in clashes with Israeli forces since October 2015, according to Palestinian figures.
Israeli authorities say nearly 50 Israelis have been killed in attacks by Palestinians during the same period.
Al-Aqsa Mosque is the third holiest site in Islam after the holy cities of Mecca and Medina.