Councillor Mike Bird said he was "extremely concerned" over the rate of infection in the town, which hit 55.8 per 100,000 people in the seven days to September 20, with 158 new cases recorded.
The rate is now higher than Wolverhampton, which is under a local lockdown banning people from visiting the homes and gardens of others who are not in their support bubble.
Councillor Mike Bird said he believed the rise in Walsall was down to people failing to stick to restrictions. He said ministers would be taking a close look at the situation in the town with a view to implementing new measures if cases did not start to fall.
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"I am extremely concerned about the rise in cases of the virus in Walsall," he said.
"The message could not be clearer. Wash your hands, cover your face and make space so we can control the virus.
"Everyone in Walsall must adhere to this message or we will get government intervention here like we have seen in other parts of the Black Country."
On August 27 just three cases were recorded in Walsall, but infection numbers have risen sharply since then and hit 23 on September 20 – the highest daily figure since May 3.
The pattern is mirrored across other parts of the region.
Sandwell saw 35 cases on both September 19 and 20 – the highest daily rate in the borough throughout the whole pandemic.
The rate of infection in Sandwell dropped to 60 per 100,000 in the seven days to September 17, but is now back up to 74.5, despite the borough being under local lockdown since September 15.
Birmingham, which is under the same measures as Sandwell and Wolverhampton, hit a daily peak on September 19, with 161 cases. The city now has a rate of 98.7.
Wolverhampton has a rate of 54.2 after 142 new cases. In Dudley the rate has increased to 33.7 per 100,000 on the back of 108 new cases, with a total of 15 cases recorded on September 20, the highest number since 19 were recorded on May 7.
The number of deaths across the region from coronavirus remain low. Of the 10 Covid deaths recorded in the seven days to September 21, eight occurred in hospitals in Birmingham. There was one death in Sandwell and one in Dudley.
Further national restrictions have started today, with pubs closing early, people told to work from home and face masks compulsory for bar staff and non-seated customers, shop workers and waiters.