Tower Hamlets Council said it would sell Draped Seated Woman after "unprecedented" budget cuts.
The work has not yet been valued but a Moore sold for £17m earlier this year.
The council said the rising threat of metal theft and vandalism made it too expensive to insure if it was on show.
The sculpture was bought by the former London County Council for £6,000 in 1960.
The bronze sculpture, nicknamed Old Flo, was installed on the Stifford council estate in 1962 but was vandalised and moved to the Yorkshire Sculpture Park in 1997.
A council spokesperson said: "With unprecedented cuts to council budgets, the council finds itself in a difficult situation and being forced to make hard decisions.
"As the borough does not have the funds required to insure or maintain the upkeep of the work, releasing these necessary funds will enable the council to support front-line services."
Tower Hamlets mayor Lutfur Rahman added: "It is with great regret that I take this decision but we are faced with a stark choice in these times of recession."
The sculpture is expected to be auctioned by Christie's in February. No valuation has been made but Tower Hamlets said estimates had ranged from £4m-£17m.
The council is having to make cuts of £100m per year over the next three years.
Richard Calvocoressi, director of the Henry Moore Foundation, said he sympathised with the council's position but added that it would be "very sad" if the sculpture was no longer on public display.
Metal theft has become a major problem in recent years. In 2005, a large Moore work was taken from the foundation in Hertfordshire, while a sundial by the artist was removed from the same location this July.
Last December, a bronze work by Barbara Hepworth was stolen from Dulwich Park in south London.
Tower Hamlets Council had considered moving Draped Seated Woman to private land in Canary Wharf but has instead chosen to "explore options" for a sale.
The auction of council artworks to meet budget shortfalls is normally frowned upon in the art world.
The last significant case was in 2006, when Bury Council was expelled from the Museums Association for selling an LS Lowry painting for £1.4m.
The Museums Association said it could not act in this instance because Draped Seated Woman was an individual piece of public art and not part of a museum collection.

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Full list of 2016-17 Danske Bank Premiership fixtures (Dates and kick-off times are subject to change by NIFL)
A major Henry Moore sculpture is to be sold by a London council to pay for front-line services after it was decided that it could not be safely displayed on council land.
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