A swastika and other symbols have been spray painted on to a recently refurbished bandstand, police said.
Humberside Police said the swastika, crude images and a swear word were painted in red at some time between midday on 5 September and 11:00 BST on 7 September at Riverside Gardens on Hook Road, Goole.
The force said it also noticed the river bank wall and steps had been sprayed and CCTV was being checked to find who was responsible.
A spokesperson for East Riding of Yorkshire Council said: “There is no place for hate in the East Riding and we are committed to taking firm action against such behaviour.”
The spokesperson added: “We have contacted the owner, Goole Town Council, to request it be removed as soon as possible and will work with them to rectify this issue.”
Goole Town Council has been approached for comment.