Passengers on board said the pilot told them there was a problem with the landing gear and that he would be making an emergency landing, according to Indian media reports.
The Dubai government's official media office said all passengers were "evacuated safely and no injuries have been reported so far" and that emergency response teams had fully extinguished the fire.
India's ambassador to the United Arab Emirates said that many passengers were in shock, adding that a crew member had been taken to hospital for treatment.
All take-offs and landings were suspended at the Middle East's busiest airport following the incident, resuming almost six hours after the crash-landing.
Passenger Alby Wilson, who was waiting in the airport lounge, said: "There was a loud noise outside. People ran to the windows and we saw the plane about 500 metres away."
"There was a lot of black smoke all across the tarmac...we were told to sit down and shortly after that there was a loud bang...the plane seemed to have shifted. The fire trucks were all around the plane."
"There is a bit of chaos here and Emirates staff don't seem to know when we can leave."
Boeing Airplanes said in a statement: "Our team is monitoring the situation in Dubai and we'll be working with Emirates to gather more information."
While Sheikh Ahmed Bin Saeed Al-Maktoum, Emirates' chairman and chief executive, posted this message online:
The airline has activated dedicated telephone lines for family members to get in contact:
UAE - 8002111
UK - 00442034508853
US - 0018113502081
16:18 3 Aug 2016
16:18 Wednesday 3 August 2016