The fire broke out at Thornes Park Stadium at 7.25pm yesterday, when the building was full of children at sports clubs.
Children were evacuated from the building mid-training, in what a Wakefield mum has described as 'a scene from the movies'.
Wakefield police say the fire broke out in the track seating area and spread to the building.
They are appealing for witnesses who may know how the fire started.
Wakefield City and North West's neighbourhood policing team said: "Arson at Thornes Park Stadium Wednesday February 26.
"Fire started in the track seating area and spread to building which was full of children at sports clubs inside.
"Appears to be a deplorable case of Anti-Social Behaviour.
"INFORMATION sought. Any witnesses to the starting of this fire urgently required !!!"
Anyone with information is urged to call West Yorkshire Police on 101 or email [email protected]