The plan - aimed at spurring economic growth - passed by a 8-3 vote with three abstentions after a marathon cabinet session in which Benjamin Netanyahu, the Prime Minister, confronted the finance minister, Dan Meridor, who argued it would cause mass unemployment.
Earlier in the day, Mr Netanyahu promised that his government would "make a tremendous revolution to allow more freedom in the area of foreign currency that has never been known before in Israel."
The broadcast did not give details of the plan after the vote. Earlier, media reports said the plan would mean restrictions will be lifted on purchases of foreign currency and Israelis will be allowed to invest and open bank accounts abroad.
The timetable on implementation was not clear, but Mr Netanyahu said on Monday that he wanted to free Israel's currency almost completely within a year.
The departure of the relatively moderate Mr Meridor could hurt the hardline Netanyahu government's sagging credibility on issues outside the economy. Mr Meridor is a longtime political rival of Mr Netanyahu's in the governing Likud Party, and many saw his presence in the cabinet as an essential counterbalance to nationalist and religious extremists.
Army Radio said a leading candidate to replace Mr Meridor as finance minister would be Infrastructures Minister Ariel Sharon, a former general and architect of Israel's 1982 invasion of Lebanon.
Mr Meridor opposed a key element of the economic plan - a Bank of Israel proposal to widen the trading band for the Israeli shekel from the current 14 per cent trading range to 30 per cent. Mr Meridor fears this will lead in the short term to a strengthening of the shekel against the dollar, harming industry, lowering exports and increasing unemployment.
In the long term, critics warn, freeing the Israeli currency could lead to a collapse similar to the Mexico crisis of three years ago.