The incident happened at Ashmore Park, Wednesfield, and has left the structure of the gate unsafe, with one pillar lifted from the ground.
It is believed the gate, on Park Way just off Ashmore Avenue, was driven into on Tuesday evening.
The vandalism has been reported to West Midlands Police.
Wednesfield North councillor Phil Bateman said: "The cost of the demolition and repair will come from local council taxpayers.
"It is a real mess, and I am sorry that it has happened.
"Vandalism is a nuisance to any community, we really do need to catch the culprits if possible.
"It goes without saying to contact the police if you witnessed this in any small part, or have any photos that you think can help them, better still if you know who it was."
Councillor Bateman added that he would communicate any outcomes with residents.
He also advised people to avoid the area just off the back off Corpus Christi Catholic Primary School.
A spokesman for Wolverhampton Council said: "The damage to the main entrance gate at Ashmore Park is extremely disappointing.
"We have reported this incident of vandalism to the police and would ask anyone who saw or knows anything about this to inform the police immediately.
"The gates have been secured by a council contractor and will be repaired in due course."
Workers from William Gough & Sons Limited were at the park on Friday to ensure the gates and structures are safe.
West Midlands Police has been contacted for comment.