The authority, which oversees the holy sites in Jerusalem, did not give any further details about the reason behind the Israeli move.
Israeli authorities have not yet commented on the news.
Al-Kiswani has been arrested and summoned several times before by the Israeli police or intelligence service.
Al-Aqsa Mosque is the world's third-holiest site for Muslims. Jews call the area the "Temple Mount," claiming it was the site of two Jewish temples in ancient times.
Since 2003, Israel has allowed settlers into the flashpoint compound almost on a daily basis with the exception of Fridays and Saturdays.
Israel occupied East Jerusalem, where Al-Aqsa is located, during the 1967 Arab-Israeli War. It annexed the entire city in 1980 in a move never recognized by the international community.
Since the beginning of the Muslims’ holy month of Ramadan, Jerusalem has witnessed skirmishes between Palestinian youths and Israeli forces due to the latter's attempts to prevent annual Ramadan gatherings and activities in the city center.