The core and legs of the 184ft sculpture - the tallest artwork in Britain - will be put into storage, while the huge steel spikes are likely to be melted down.
B of the Bang, near the Sportcity stadium in East Manchester, has been plagued by safety problems since it was commissioned to mark Manchester's Commonwealth Games triumph in 2002.
Nine of its 180 steel spikes have been removed after one fell off, and around £300,000 was spent to make the rest safe.
Now the council's ruling Labour executive has voted to dismantle the sculpture while they consider its long-term future, possibly having new spikes made and being erected at either the same site or at another area near the stadium.
Thomas Heatherwick, who designed the original, will continue to try to come up with an alternative - and safe - design. His preferred option is to replace the steel spikes with lighter, carbon-fibre versions at a cost of up to £3m.
But council leader Sir Richard Leese said no more council tax payers' money would be spent on B of the Bang.
The sculpture cost around £1.7m - money that was recovered from Mr Heatherwick and his consortium in an out-of-court settlement.
The funds came from a number of public-sector sources, including the council, and would probably be available to rebuild B of the Bang. Privately, senior council sources admit it will be difficult or impossible to raise the additional £1m-plus needed to fund the project.
Sir Richard said: "We have committed ourselves to continue to work with the artist to determine whether there is a robust and affordable strategy for the re-construction of the structure.
"We have, however, made it clear that the will be no city council funding made available to support its rebuilding."
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Dave (12/02/2009 at 08:40)
It's only been about 3 or 4 years since the first spike fell off, so I suppose they can't be too hasty in taking it down. I do love the attitude of the Council. "Oh my God, spikes are falling off and could kill people, quick let's call a committee meeting for a few months time and discuss what meetings we'll have to discuss the matter"