Dr Lisa McNally, director of public health for Sandwell, said the council will close any location which is a threat to the public.
Powers granted to local authorities last Thursday mean local authorities can shut any building, event or public outdoor place without notice.
The latest data shows the rolling seven-day rate of new Covid-19 cases in Sandwell has increased from 8.6 per 100,000 people to 22.3 after 73 new people tested positive.
Dr McNally warned: “If we find a venue has a large number of Covid cases associated with it, then we will close that venue.
“We have always been able to do that it but it is much quicker now.”
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Her warning comes after 40 new cases were reported in Smethwick in seven days. Saying that although the number of cases are lower than in Leicester the rate of infection is faster, she added: “We haven’t seen those sort of rates since the beginning of the pandemic back in April.
“These cases have arisen in one week which is quite remarkable.
“It is the speed and scale of the rise that is different in this situation.”
The new powers do not allow the blanket closures seen during the national lockdown but senior council officers can now shut anywhere they believe is a threat to public health.
Significantly, they can close premises without seeking approval of the government or local councillors.
Over the last month, Sandwell has seen outbreaks in schools and factories, the latest at CBS Packaging in West Bromwich where a third of the workforce tested positive.
Saying businesses or groups like places of worship should contact the council as soon as they learn of infections, Dr McNally added: “Will only use these powers if outbreaks get out of control.
“If locations like workplaces contact us, we can work them to control infections and hopefully avoid the need for closures.
“The most import thing of all is if you have symptoms, which is a cough, a high temperature or a change in how you taste food, you should absolutely stay at home.
“Do not go to work, do not go shopping or go to college because if you do it could cost lives.
“Self isolate and get a test as soon as possible either at home or at a testing centre.”
Asking people in Smethwick to take extra care, she added: “Only go out if you have to, if you have the choice stay home.
“If you have to go out you should be very, very careful to keep your distance from others, preferably two metres.
“Wear a face covering whenever other people are about, like on public transport or in a shop.”
Anyone with coronavirus symptoms can book a test by calling 119 or use the NHS 111 online service.