Wolverhampton Council leader Ian Brookfield issued the stark warning as coronavirus cases surge in the city and deaths continue to rise.
He said the premises flouting the rules are "risking lives" and urged residents to be the council's "eyes and ears".
He said: "We are facing a very grave situation and we need everyone to understand this is serious – families and lives are at stake.
“Premises flouting the rules are risking lives – it’s as simple as that. We need to know about this so that our enforcement officers can work with local police to take action and stamp it out.
“We need local people to be our ‘eyes and ears’ on the ground. If you see something in your workplace or when you are making an essential visit to your local store – we need to know about it.
"Retailers and workplaces must do everything they can to keep their staff and customers safe – and customers should wear a face covering and follow social distancing measures.
“The council has also written to city supermarket managers urging them to do everything within their power to make stores safe for employees and customers.
“We’re still getting reports of far too many shoppers in one store at any one time. You have to question what has happened to the controls that used to be in place.
"We’re still getting reports of people not wearing face coverings. This is unbelievable given where we are."
He added: “My message to customers alarmed or concerned with what they see in premises is ‘vote with your feet’ - don’t put yourself at risk and report it to us so we can take action. To those who think they are above the law, obey the rules or face a fine.
“Complacency is a killer and we’ve all got to up our game. This is not a step we are taking lightly. It’s a last resort, but it emphasises the gravity of the situation.
"It’s vital that we all obey the rules and that we all double down on our efforts to stop the spread of Covid-19. That means following the lockdown restrictions and avoiding any unnecessary contact with others.”
Wolverhampton Council issued a £1,000 fine to a carpet store which continued to trace and allow customers inside during lockdown and served it with a prohibition notice.
Since March, eight prohibition notices have been served on businesses by the council for breaking Covid rules.