A 15-year-old boy has been arrested on suspicion of burglary and criminal damage.
Gwent Police received a call at around 8.40pm on Thursday after windows were smashed at All Saints Primary School, before around £100 in cash was reportedly stolen from the building.
Damage was also later reported to the B&M store on Bethcar Street and Poundstretcher on The Walk at around 9.40pm.
Officers arrested a 15-year-old boy from Ebbw Vale on suspicion of burglary and criminal damage and he is currently in police custody.
A dispersal order has also been issued for the area following reports of anti-social behaviour.
Inspector Shane Underwood said: “Officers are currently completing all necessary enquiries to take positive action against those responsible for the recent acts of mindless damage, crime and disorder in the town centre, and patrols will continue throughout the weekend.
"This type of behaviour will not be tolerated, and we'll take action against anyone causing harm in our communities.
“If you were in Ebbw Vale yesterday evening and saw anything you believe can help us with our investigation, please get in touch.”
“I also ask that parents ensure they know where their children are at all times, particularly when the order is in place.”
The dispersal order is now in effect and will be in place until 7.40pm on Saturday 15 January.
The order gives officers extra powers to direct groups to leave the area if their behaviour is likely to contribute to disorder or cause harassment, alarm or distress to members of the public.
If individuals return to that area after being moved on, they will be arrested.