The rate of infection in Greets Green and Lyng ward is 108 per 100,000 people with 15 new cases in the last seven days of data from March 30 to April 5.
Comparable figures for the same period in Newton ward show an infection rate of 103 per 100,000 with 13 new cases.
The rates are more than twice the current average rate for Sandwell which is 39 new cases per 100,000.
Anyone showing symptoms must self-isolate and book a Covid-19 test at www.gov.uk/get-coronavirus-test or by calling 119.
Dr Lisa McNally, Sandwell’s director of public health, said: “In recent weeks, Sandwell has seen one of the fastest falls in Covid-19 case rates in the country. This is a great achievement by the local community.
“Recently, however, we have seen a sharp rise in infection in these areas.
“There has been no single large outbreak - rather there has been a general rise in infections, with sometimes several cases within one household.
“People living and working in these areas must take extra care to avoid becoming infected and passing Covid-19 on to others.
“In particular, if you have Covid-19 symptoms, stay home and book a test. If we don’t self-isolate when we have symptoms we can put other people’s lives at risk.
“This is especially important as the variant of the virus first found in Kent that is circulating in Sandwell spreads very quickly and is linked with a higher risk of severe illness and death.”