A greater police presence will be seen in the Merry Hill centre and both Stourbridge and Halesowen town centres as a result of the order, West Midlands Police said.
The order, which grants police greater powers to break up groups, began on Sunday and will run until tomorrow.
It comes as Government restrictions were relaxed further today, so non-essential shops and outdoor hospitality are allowed to open.
Gatherings of two households or up to six people are currently allowed under coronavirus lockdown laws, but any larger groups are not permitted.
Matthew Turner, PCSO in Dudley, said: "The following dispersal order has been issued for all officers to carry out from Sunday until the PM of Tuesday 13th April 2021. As a result a greater police presence will be seen in all areas.
"S.35 Dispersal Powers have been authorised, giving officers the power to disperse any persons committing or likely to commit antisocial behaviour. Any returning persons will face arrest.
"These powers will cover the Merry Hill centre, and both Stourbridge and Halesowen town centres."