A Muslim clerical trust known as the Waqf runs the compound under Israel's overall security control.
Yusuf Natsheh, director of the Waqf administration, said the Waqf was not consulted about the plan to shut down the walkway, which he called a "disastrous" policy liable to touch off protests.
"This is a very sensitive issue," he said. "It is so close to the mosque, and Palestinians, Arabs, Muslims ... all over the world will be unhappy."
They think Israelis are "eradicating their historic road, they are eradicating their heritage" under the guise of security concerns, he said.
Nearly five years ago, hundreds of Israeli police fired stun grenades and tear gas to disperse thousands of Muslim worshippers who hurled stones, bottles and trash in outrage over earlier Israeli repair work in the area.