It happened between 6.30pm and 9.30pm on Monday at Ceara School in the Sloan Avenue area.
Fencing, potted plants, a tree, lawns and foundations of building work have all been damaged.
Police said three young males entered the grounds of the school that caters for children with special needs.
Dr Peter Cunningham, the school's principal, said: "I'm absolutely horrified at the considerable damage, this is a special school and the parents have enough to deal with without this added annoyance."
"It's an attack on the local community. Work on an extension which we have long campaigned for, costing over £500,000 will now have to be put back at least three weeks."
Christine McCaughey's son Blake, aged 5, goes to the school.
She said:"They don't realise how much of an interruption this is to the parents and the hundreds of children that it directly affects."
"We rely on this school and for them to come in and do what they've done without a second thought, it's disgusting."
Sinn Fein Councillor Johnny McGibbon says the community is outraged: "The community will be shocked and angered to hear of this attack upon Ceara School and the damage caused."
"The delinquents responsible started up and used heavy plant machinery from the site during their rampage and in doing so put themselves and others at grave risk," he continued.
Mr McGibbon said, "This is totally unacceptable behaviour and those responsible must be brought to book."
Police have issued descriptions of the suspects. One boy is described as being between 5'4"-5'6" tall, wearing a black hoody and black tracksuit bottoms.
Another suspect was approximately 5'7" tall, wearing a red hoody and dark tracksuit bottoms.
The third assailant is approximately 5'11"-6'1" tall and wore a green hoody with grey tracksuit bottoms.
Police are asking anyone with information to contact them at Lurgan on 0845 600 8000.