Witnesses are being sought after the bandstand in Hotham Park was vandalised on Friday night (May 31).
According to Arun District Council, thousands of pounds of damage has been caused.
In a post on social media, the district council's Arun Parks and Greenspaces team wrote: "We and the Hotham Park Heritage Trust are extremely saddened to report the thousands of pounds of damage caused to the bandstand in Hotham Park by vandals on Friday night.
"If anyone has information which may assist in identifying the suspects, please contact Sussex Police quoting police reference 1677 - 31/05/19."
The district council said it is 'working quickly' to repair this 'important community and heritage asset'.
It added: "We have erected some temporary barrier fencing to ensure people can continue to use the bandstand safely. Contractors are sourcing materials with aims to have the structure back in use as soon as possible."
Sussex Police has been approached for comment.