Edinburgh City Council said the Jawbone Arch in the Meadows, on the city's south side, would be taken down so the whale bones can be stored ahead of repair work.
The bones are being removed later this month in a bid to secure the future of the arch, which has stood in the park for more than 100 years.
They will be stored for up to six months to allow them to dry. Experts will then assess their condition.
The area surrounding the Jawbone Arch will be cleared of fencing to allow better pedestrian and cycle access in time for the Festival season.
The estimated total or the repair work is £49,000, with more than half of the target being provided by the council and Edinburgh World Heritage.
Additional support from the Marchmont and Sciennes Community Council, the Grange Association, the Friends of the Meadows and Bruntsfield Links, and a range of individuals has also been pledged. But the shortfall is £20,000 and fundraising is ongoing.