Thirty-four new cases have been confirmed in the past seven days, with people urged to take the situation "seriously".
Sandwell Council says the virus is spreading due to multiple cases in households and extended family gatherings.
It comes as the local authority said that an outbreak at a DPD hub in Oldbury - which was revealed this month - appears to have been contained.
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The borough's director of public health, Dr Lisa McNally, said: "We are seeing a large number of household clusters in Smethwick – those are households with four, five or even six cases – often within multi-generational households.
"We have also had a number of outbreaks in Smethwick businesses which have spread into the community."
Residents have been advised to use separate bedrooms and avoid sharing towels to "avoid having one person in a house infecting everyone", said Dr McNally.
People have also been urged to take tests if they have symptoms of Covid-19, and avoid close contact with others if they test positive.
Fresh warnings about a rise in cases in Smethwick were first revealed by the council on Tuesday.
Businesses have also been reminded of the important of safety guidelines.
The advice has been published in a range of languages, Dr McNally added.
Sandwell Council's interim leader, Maria Crompton, said: "We are working intensively in Smethwick with community leaders, faith leaders and businesses to get the message across.
"I’d urge people not to arrange get-togethers, not to visit one another inside their homes and to make sure they wear masks in shops and in on public transport."
She added: "Cases in Smethwick are continuing to rise and we have more cases in the Smethwick area than any of Sandwell’s other towns.
"Covid-19 is a potentially fatal illness. We need people to take things seriously and prevent the spread of the virus."
An outbreak at DPD, in Broadwell Road, was reported on August 14 where 19 workers had tested positive at the time.
The total number of workers who have tested positive has now risen 31 after Sandwell's health teams carried out proactive testing.
The council says no more testing is planned at this stage. A number of DPD employees are continuing to self-isolate.
Dr McNally added: "It was always likely more positive cases would be identified with the proactive testing and that’s helpful to everyone’s efforts in preventing further transmission to others."
Dwain McDonald, chief executive at DPD, added: "We’re very grateful to Sandwell Council and Dr Lisa McNally and her team for their support.
"Our priority is always the safety and well-being of our people.
"The team in Oldbury and Public Health England have been fantastic and we are pleased that the testing has been completed quickly and efficiently."
The DPD site includes a regional distribution hub as well as a local delivery depot.
Health officials say the risk of catching coronavirus from parcels remains extremely low.