Officers urged parents to monitor the movement of their children after trouble was reported amid the introduction of the new national pandemic lockdown.
Reports of large groups of "youths" damaging property and throwing objects at shoppers in Liverpool city centre were received by Merseyside Police, leading the force to warn there had been an increase in anti-social behaviour.
Those involved were also accused of "engaging" with drugs.
The concerns led to police chiefs signing off the creation of a dispersal zone across much of the city centre.
Find out where you can receive the Covid-19 vaccine by typing in your postcode below
The move allows officers to ask anyone they believe may causing trouble to leave the area. If they are caught returning while the order is in place, they could face prosecution.
Liverpool ONE, Lord Street, Queen Square, Williamson Square, Lime Street and Hanover Street were all included within the area under the measures, introduced on Tuesday.
They will run until Wednesday afternoon.
Detailing the move, Merseyside Police said on Twitter: "There has been a increase in anti-social behaviour in the city.
"Large numbers of youths causing damage, throwing items at people and engaging in drug use. We have introduced a dispersal zone... We are now in national lockdown, parents please know where your children are."
