Prime Minister Benjamin Netanyahu ordered the footbridge between the Western Wall and the religiously sensitive Temple Mount taken down, the official said.
The order followed a request by Jordan, which has custodial rights to Muslim holy places in Jerusalem, said the official, speaking on condition of anonymity because of the sensitivity of the issue.
However, the footbridge was still standing by early on Thursday afternoon and it was not immediately clear when work would start to dismantle it.
The Temple Mount is the holiest site in Judaism. Known to Muslims as the "Noble Sanctuary", it is Islam's third-holiest site.
Previous attempts to change its status or assert Jewish claims to it have frequently resulted in violence, including in 2000 when a visit there by then Israeli opposition leader Ariel Sharon provoked widespread Palestinian rioting and helped spark the second Palestinian uprising.
Sharon became Israeli prime minister in 2001. He died in early 2014.
The Israeli official said that Jordan expressed its concern to Netanyahu when construction on the bridge went ahead two weeks ago and "he agreed to its request" that it be dismantled, adding that no official approval had been given for the project.
Jordan signed a peace treaty with Israel in 1994, the second Arab country to do so after Egypt.

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