Before the cabinet vote, Ehud Olmert, Israel's prime minister, said in broadcast remarks that the ramp was a dangerous structure that needed renovating.
He said: "There is no religious issue here" and accused "Arab extremists" of inciting violence.
In East Jerusalem, Israeli police confronted protesters for a third straight day and arrested five, said Micky Rosenfeld, a spokesman for the national police.
The Arab League condemned the dig at a meeting in Cairo on Saturday and demanded Western nations force Israel "to stop this aggression immediately".
The Jerusalem compound has frequently been a flashpoint for Israeli-Palestinian violence.
A Palestinian uprising erupted in 2000 following protests at the complex after Ariel Sharon, then a candidate for the prime minister's post, visited the site as head of Israel's opposition party.
Israel captured East Jerusalem in a 1967 war and annexed it in a step not internationally recognised.
Palestinians want the eastern part of the city as the capital of a future state.