Families hoping to access the play area and route around the lake in Mary Stevens Park in Stourbridge have been met with a cordon on Tuesday and Wednesday.
It comes after the discovery of dead birds in the park, as well as across the borough.
Councillor Ian Bevan, cabinet member for public health, said: “We’ve had a number of reports of dead birds in Mary Stevens Park [on Tuesday], so we are liaising with Defra and the UK Health Security Agency (UKHSA) West Midlands concerning their safe removal and taking further advice.
“As a precautionary measure, the council has closed off a number of areas within Mary Stevens Park, including pathways around the lake and the children’s play area.
“We urge members of the public not to touch or let pets near to any dead or poorly wild foul. Instead, please report any sick or dead birds that you see to Dudley Council Plus on 0300 555 2345.”
Deputy Mayor of Dudley, Andrea Goddard, added: "Areas of Mary Stevens Park have been closed off today. This includes the play area and the pathway around the lake.
"This is a precautionary measure after three dead birds were found in the park [on Tuesday] morning close to the children’s play areas.
"At this stage it hasn’t been confirmed as avian flu, but we are working closely with the UKHSA and Defra to ensure we are following guidance and taking precautionary measures.
"The risk to people’s health is low but it can be spread through close contact, which is why it’s important people keep their distance.
"We are working on joint communications with the UKHSA to residents and will be sharing messages via the council’s social media channels.
"As you can imagine, this is a fast-changing situation and as soon as we know more, I will share details with you.
"Please do not hesitate to get in touch if you have any questions and help us spread the important message that people should stay away from dead or poorly birds."
Cases of bird flu are also suspected but not yet confirmed at Himley Hall and Lakeside in Withymoor.
Dudley Council said: "At the moment, we are unable to confirm the cause of death but birds have been sent away for testing.”
Bird flu has been found at scores of poultry farms and commercial premises across the UK in the past year, while the disease has also ripped through breeding colonies of seabirds, killing thousands in some sites.
The UK Health Security Agency (UKHSA) has said avian influenza is primarily a disease of birds and the risk to people's health is very low.