Flaming shrapnel from the fireworks rained down on a residential area behind the Chinese temple in Suphan Buri provincial town, northwest of Bangkok, where the official event was taking place.
"We think the explosion was an accident. The fire is under control but we will keep monitoring it," said local police commander Reera Butrpho.
He said those killed and some of those wounded had been among spectators watching the finale of the fireworks display when the explosion happened.
The resulting blaze, which tore through a row of wooden houses near the event, also caused several injuries, police said.
Images broadcast on Thai television showed homes and vehicles engulfed in flames and people being rushed to hospital on stretchers.
Thailand's TNN channel reported that the three killed were part of the firework team and one injured person was in a critical condition.
One witness, Krianee Kitpat, said she was standing in front of her home when the accident happened.
"I saw the fireworks coming directly towards my house and ran inside," she said, explaining that she was injured by shards of glass as the impact of the projectile shattered a fish tank.
Suran Sahaidee, a monk from a nearby Buddhist temple, said the blast happened in the third display of the evening.
"The fireworks exploded at a low level and then fell into a tent where they were storing the fireworks and it caused a huge blast and a fire," he told TNN.
The news report said 20 homes were completely destroyed in the blaze and a further 30 were damaged.
Suphan Buri governor Somsak Phureesrisak said he had ordered tents to be set up near the residential area, believed to comprise of around 100 houses, but did not give details of the number of people evacuated.
"People do not want to stay too far away from their homes because they are concerned about their property," he said.
The New Year celebration was attended by Deputy Prime Minister Chumpol Silpa-archa and his brother, former Thai Prime Minister, Banharn Silpa-archa. Neither were believed to have been hurt.
Thailand has a large ethnic Chinese population and the advent of the Year of the Dragon has been widely celebrated across the country.