It was found during one of two separate security alerts which caused major disruption in counties Down and Armagh, forcing a care home and three schools in total to be evacuated.
The alert at Ceara School on Sloan Street in Lurgan ended after a controlled explosion was carried out on a suspicious device, which has been declared a "viable explosive".
Police believe it was left there by dissident republicans. It has now been removed for testing.
Chief Inspector Anthony McNally, Area Commander for Craigavon, said: "This device was designed to kill or maim anyone close by, police officers or local people alike.
Police believe that dissident republicans were responsible for leaving this device and would appeal to anyone who has any information to contact them at Castlereagh on 0845 600 8000.
Chief Inspector Anthony McNally
"Those responsible showed blatant disregard for the local community and put the lives of local people, indeed local children at risk. We are very fortunate no-one was killed or injured."
A bomb threat had been phoned in overnight, according to the school's principal.
"I'm of an age where we had the troubles, and schools right in the midst of the troubles were always seen to be places where children could come and fell safe," Dr Peter Cunningham said.
"I think anyone who puts a device, be it a viable device or a hoax, into a special school - I think we have hit a new low in this country."
Dr Cunningham said that routine was everything to the children at his school and the disruption the alert has caused would affect them.
He added: "I am so profoundly disappointed. My children, who all have severe learning difficulties, have never done harm to anyone and for anyone to do this to us is just despicable."
Sloan Street has reopened after being closed for most of the day.
Around 300 pupils at Carrick Primary School were also unable to attend school due to the police cordons.
Education Minister John O'Dowd has condemned those behind Friday's attack.
The Sinn Féin minister said: "I, along with the rest of the community, am disgusted by the actions of those who planted a bomb at Ceara Special School in Lurgan this morning.
This attack was against the most vulnerable in our society and is a clear indication of the contempt that those responsible hold for the entire community.
Education Minister John O'Dowd
"There is no more stark contrast when you look at the action of the bombers and the actions of those who work in Ceara School day after day caring and loving for their pupils.
"Ceara School, its staff, pupils and parents represent everything we can be proud of in our community. Those behind this attack are the direct opposite of everything Ceara stands for."
DUP MP David Simpson, who was at the scene, said: "For someone to take a device and leave it in that area beside a special needs school, it's crazy. The mentality is unreal and it's causing major problems in this town today."
Chief Inspector McNally continued: "I would like to thank to local residents and wider community in the area for their patience and support throughout this operation and I want to reassure them that we will not be deterred by this attack.
"We will continue to deliver the personal, professional and protective service that the vast majority of residents in the Lurgan area want to see."
Meanwhile, the separate alert in Holywood ended after bomb experts examined a suspicious object and declared it to be an "elaborate hoax".
Residents have been allowed to return and roads have reopened following the evacuation of Holywood Nursery School and Abbeyfield House sheltered accommodation.
Gordon Dunn, DUP North Down MLA, said his constituency office was among properties evacuated at Church Road.