Friends of Rowntree Park say vandals poured paint around the park – including on the grade II-listed lychgate and dovecote containing First and Second World War memorial plaques.
Posting on Facebook, the group say people broke into the park yesterday evening, Monday May 24.
They say a wheelbarrow, bird feeders and poles have also been taken.
On Facebook the group wrote: “Sad to report that our store was broken into yesterday evening and the war memorial vandalised.
We have had a wheelbarrow taken and some paint poured around – including the lychgate in the park (the Grade II listed war memorial construction known to some as the dovecote).
“Also, we’ve had bird feeders and poles taken.
“There is a fair amount of mess and destruction for no real reason other than ‘a bit of a laugh’. Sad times…”
The post noted that volunteers tried to clean up the mess but chemicals will be needed to remove the paint.
They said the incident has been reported to the police and council.
Historic England listings say the lychgate and dovecote containing the war memorial plaques were installed in 1921 and are likely to have been designed by Frederick Rowntree or W Swain for Rowntree & Co Ltd and presented to the City of York as part of the memorial Rowntree Park.
The memorials commemorate Rowntree Cocoa Works’ employees killed or injured in the First World War and, subsequently, to honour those who died in the Second World War.
City of York Council has been approached for a comment.