Israeli public broadcaster KAN said the closure will remain in place until the end of the Jewish Passover holiday on April 12 due to the security situation.
Exceptions will be made for humanitarian and other outstanding cases, a statement by Gallant said.
The decision cancels all facilities made for the Palestinians during the Muslim holy month of Ramadan for access to the Al-Aqsa Mosque complex in occupied East Jerusalem, the scene of violent Israeli raids over the last week.
Tension escalated across the Palestinian territories in recent days after Israeli forces stormed the Al-Aqsa complex and forcibly removed worshippers for two nights in a row on Tuesday and Wednesday.
The Israeli raids on the mosque triggered rocket fire from the Gaza Strip and Lebanon, with Israel retaliating with air and artillery shelling.