The alarm came in around 2.30am, Mats Körner of the Greater Stockholm Fire Brigade (Storstockholms brandförsvar) told Sveriges Radio (SR).
"Night-watchmen discovered the fire in the school entrance. It spread inside the building and to the attic," said Körner.
Police are investigating claims that New Year rockets had been set off inside the school at the time of the fire.
There were several other incidents involving fireworks around Greater Stockholm ahead of New Year's Eve.
In Sweden, the age limit for buying and handling fireworks is 18. But according to news agency TT, nine out of 10 patients taken to emergency wards with injuries from fireworks are under 18.
It is also illegal to let under-18s light fireworks, but the risk of prosecution is basically non-existent, according to TT.
Åke Persson, a fireworks expert at the Swedish Fire Protection Association (Brandskyddsföreningen), said the police should be more vigilant.
"It would be good if we had some criminal cases so that we can develop judicial practice around the issue," said Persson.
Several authorities also warned of health risks associated with fireworks.
Writing in medical journal Läkartidningen, several doctors called for a ban on the most powerful fireworks, saying they can cause more serious injuries than previously thought.
"How many body parts have to be sacrificed?" the doctors asked.
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The Swedish Environmental Protection Agency (Naturvårdsverket) claimed fireworks are a health and environment hazard.
The Agency said 300 tonnes of tiny particles were released from New Year's fireworks in 2011.
Although that represents just 1 percent of the total 29,000 tonnes of particle emissions in 2011, experts at the agency urged the public to be cautious over New Year's.
"When you breathe in, the particles could enter your lungs and cause health problems," Maria Lidén, the agency's coordinator of international reporting on air- and climate issues, told technology magazine Ny Teknik.
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