Despite the blaze at the Address hotel, the display at the nearby Burj Khalifa, the tallest building in the world, started as planned at midnight.
Officials say the fire has been brought largely under control and 16 people suffered mostly minor injures.
It is unclear what caused the blaze, which broke out as large crowds had gathered to ring in the new year.
People were asked to leave the area around the Address Downtown Hotel, which was evacuated.
The fire broke out at about 21:30 local time (17:30 GMT) and appeared to engulf much of the building, a five-star hotel and apartment complex, within 10 minutes.
It started on the 20th floor, officials said, and had not spread inside the building, they claimed.
The Dubai government tweeted that 14 people had suffered minor injuries, one moderate injuries and there was one "heart attack case" due to "overcrowding and smoke".
Irish singer Anita Williams, who was performing at the hotel when the fire began, told the BBC that people left in a "stampede".
"We left everything. There was debris falling down. It [the fire] just shot up through the entire hotel.
"Everybody was screaming, everybody was running... I thought: 'This is a film'."
The fireworks display went ahead as smoke continued to billow from the hotel.
Alternative accommodation would be offered to evacuated guests, the Dubai government said.
The BBC World Service Middle East editor, Sebastian Usher, says the display is a huge prestige event for Dubai, and authorities want the images that people look back on next year to be of the fireworks - and not of the blaze.
Tom Stroud, from London, who is staying near to the hotel, said: "It happened so quickly. There was smoke billowing everywhere and people running away."
A tourist, Michelle Duque told the BBC: "All of a sudden we saw this huge black plume of black smoke coming between the Khalifa Tower and the hotel.
"The flames burst out really big and before we knew it the whole of the Address Hotel was covered in orange flames."