She said: "We are hugely saddened by the loss of our pupil. This lovely little boy was a huge part of the school life, lively and always smiling.
"The whole school community is coming to terms with this tragic news and we are holding our memories of a very popular little boy, full of character and energy.
"He will be missed by all of his friends with whom he loved playing tag and football. His family are in our thoughts and prayers at this time. He will be deeply missed by all."
Paul Matthews, chief executive of Monmouthshire County Council, said: "This is just the very worst thing. The whole organisation has been rocked and finding words is so very hard.
"There will be much to do in the coming days and we will play our part to the best of our ability working closely with Gwent Police and other agencies."
Council leader councillor Peter Fox said: "I would like to offer deep and sincere condolences to the family and friends of this little boy from everyone associated with Monmouthshire County Council.
"It is just not possible to put into words how sad we feel. We are here to help and will be supporting the school, children and colleagues over the coming days and for as long as is necessary."
A seven-year-old boy has died after being hit by a council mini bus, police have said.
The primary school pupil, who has not been named, died at the scene about a mile from Osbaston Church in Wales School in Monmouth after the end of the school day on Monday.
On Tuesday, Gwent Police said the mini bus driver, a 45-year-old man from Gloucester, had been arrested on suspicion of causing death by careless driving and remained in police custody.
A spokeswoman said: "Emergency services were called at around 3.40pm yesterday to reports of a road traffic collision between a minibus and a pedestrian on Hereford Road, A466, Monmouth.
"The pedestrian, a seven-year-old boy, sadly died at the scene. His family are being supported by specially-trained officers.
"The driver of the minibus, a 45-year-old man from Gloucester, has been arrested on suspicion of causing death by careless driving. He remains in police custody at this time.
"Officers are investigating the circumstances surrounding the incident and are appealing for anyone who may have witnessed the collision or if anyone has dash cam footage from the area around the time of the collision to please contact us."
A statement from headteacher Catherine Jones said the school was "coming to terms" with the loss of the little boy, who she described as "lively and always smiling".