A large fire broke out at the former Elmete Wood School in Roundhay at 6pm on Saturday, destroying the roof of the building.
Residents were advised to keep their windows and doors shut as firefighters spent the entire night tackling the blaze, which was seen from up to a mile away.
Watch commander Tim Pallister said the school, which closed in 2016, will now likely be demolished.
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Local resident Sara Dawson, who is a member of community group Friends of Roundhay Park, said the building had recently attracted a raft of anti-social behaviour.
Pictures shared with the group on social media appear to show barbecues left at the site, as well as blankets and graffiti inside the building.
Sara said: "We are aware of anti-social behaviour in the building and we’ve seen images of the inside showing barbecues, blankets and graffiti.
"Since the first lockdown, people are exploring further and deeper into Roundhay Park and discovering new areas.
"Most people treat the area with respect and use it as they should, but sadly there are a small minority of people who mistreat it."
Sara, who lives near the Elmete Wood site, said that reports of litter and anti-social behaviour in the area had increased since the first lockdown.
She added: "The park has never looked as trampled as it has during this last year. The levels of litter and dog mess are at an all time high.
"But Roundhay Park is still one of the city's safest parks and we’d like to thank everyone who uses it as they should and treats it with the respect it deserves - it is everyone’s responsibility to look after it."
A spokesperson for West Yorkshire Police said an investigation into the fire was ongoing and police are expected to release an update on Monday.