It follows complaints over gangs of young adults gathering in Llangefni, drinking alcohol and causing criminal damage.
The power allows police and community support officers to force troublemakers to leave.
The order will remain in force until 01:00 BST on Sunday.
"The action we are taking is twofold," explained Sgt Tracey Llewellyn, from Anglesey's Safer Neighbourhood policing team.
"Initially we would like to reassure those living in or visiting the town centre that we are taking positive action against youths causing repeat issues of anti-social behaviour in and around the town to ensure that they are not plagued by the behaviour of certain youths.
"Equally importantly is to protect young people from the excesses of alcohol and its potential consequences."
The dispersal order means any person under 16-years-old can also be taken home, or to a place of safety.
Individuals can also be banned from the area for up to 24 hours, or face arrest if they return.

The cinema chain has "provided the British public with unforgettable, cinema experiences", Bafta said.
The awards will be held at London's Royal Albert Hall on 12 February.
The Outstanding British Contribution to Cinema award is presented annually in honour of Michael Balcon, the British film producer known for his work with Ealing Studios.
Previous recipients include Mike Leigh, Sir Kenneth Branagh, Working Title Films, Sir John Hurt and BBC Films.
Curzon's history stretches back to 1934 with the opening of its first cinema Curzon Mayfair.
Dame Pippa Harris, chair of Bafta's Film Committee, said: "I am thrilled that Bafta is honouring Curzon with the Outstanding British Contribution to Cinema Award.
"For over 80 years, Curzon has provided the British public with unforgettable cinema experiences, while championing independent, art house and foreign language film-making.
"I would like to thank everyone at Curzon for their extraordinary contribution to our industry, and for their unwavering commitment to bringing the very best in film to audiences across the UK.
Philip Knatchbull, Curzon's chief executive, said he was "delighted" at the award.
"Curzon has a long and proud history in the British film industry and many talented and passionate people have contributed to its success story over the years," he said.
"We think of ourselves as champions of bold and visionary film-making from around the world supported by our growing network of cinemas and home cinema digital platforms."
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Youths gathering in an Anglesey town centre face being ordered to move, after police imposed an anti-social dispersal order in the area.
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Curzon will receive an outstanding British contribution to cinema prize at this year's Bafta film awards.