Sandwell Council has written to residents outlining proposals to redevelop land off Goldicroft Road, in Wednesbury.
The local authority said it will fence off the park for 10 days while it carries out "ground investigation works".
It has prompted the launch of a Facebook campaign group, called Friends of Goldicroft Park, and also a petition, which has attracted more than 150 signatures.
Nick Jardine, 57, who launched the group, said: "Everyone is up in arms about it because everyone is in the dark, no one has been told anything.
"I set up the page to let people know what is going and get a bit of opposition to it. This has been a park since 1916.
"The story goes that someone gave the park to the council and wrote it into a covenant to say it has got to be kept as a recreational ground.
"We have had that letter through and everyone has got mad about it because they [the council] have just gone ahead without consulting everyone.
"They have done it totally the wrong way round. Not many people trust the council, they think it will go behind peoples' backs and build on the park."
Site work was due to begin on Thursday but that has been postponed by three weeks while Sandwell Council carries out research into whether a covenant exists.
Work is now due to start on June 21.
The letter, which was sent to residents on May 18, said: "Sandwell MBC will be undertaking ground investigation works on land off Goldicroft Road, Wednesbury.
"Works will inform the suitability for the redevelopment of the site for housing."
The park, which is surrounded by residential properties, is popular with dog walkers and features grass, trees and bluebells.
It has been used by generations of people within the community.
Sandwell Council said "all working positions will be fenced for the duration of the work", meaning access to the green space will be limited.
Work will take place from Monday to Friday, between 8am to 5pm.
A public meeting was held between residents on Tuesday evening where concerns were raised. About 35 people attended, along with Wednesbury North councillors and West Bromwich West MP Shaun Bailey.
Councillor Luke Giles, one of the Wednesbury North councillors, told the Express & Star: "I will do everything possible to stop this development from happening.
"We need more green spaces, we need to preserve the green spaces that we have and not get rid of them. The council need to take a forward and smart approach when it comes to developing.
"Not by taking green spaces away from us. I will be lobbying the leader of the council and asking to meet up for a chat and a way forward."
Fellow ward Elaine Costigan said she was "fully" supporting residents, adding: "The residents will not want to lose this green space. We think there is a covenant on there."
Sandwell Council was approached for comment.