The flood boat pavilion in Moorhouse Park will be pulled down during the Nowra Bridge upgrade because it is too fragile to relocate.
A Transport for NSW spokesperson said engineers conducted an assessment of the arch and it wasn't able to be moved to another site.
"An assessment of the Captain Cook Memorial concrete arch indicated it couldn't be relocated during work to build the new Nowra bridge due to the construction type and size of the structure, and as such it will be removed," a spokesperson said.
"Transport for NSW carried out an archival recording to document the details of the structure."
It believed a time capsule may have been buried near the base of the structure, and Transport for NSW will try to find the capsule and return it to Shoalhaven City Council and the Shoalhaven Historical Society.
Arthur Moorhouse, son of Frank Moorhouse (after whom the park was named), said it was a shame nothing had been done with the structure.
"I had plans for it, to put a display of agricultural equipment with the vandal proof fencing over it and the council even gave us some funds towards doing it," Mr Moorhouse said.
"Then they changed councils and the new Mayor wanted us to find somewhere else for it."
The flood boat pavillion was was erected at Moorhouse Park in 1971 to mark 200 years since Captain Cook landed in Botany Bay.
Government funding was received for restoration of the flood boats and the southern one called 'Shoalhaven' was used in the re-enactment of Captain Cook's landing at Botany Bay for the bicentenary in 1970.
It then became the focal point of Nowra's memorial for that anniversary, placed in a custom-made boatshed in Moorhouse Park near the southern end of the Nowra Bridge.
Vandals damaged the site and historic boat so it was removed for restoration in 2001 and then relocated.