NBC News, which reported the deaths, said dozens others were injured in the incident late on Sunday.
The news channel said that the fire truck was manned by police officers, citing sources.
It had earlier said a sergeant and an officer had broken limbs and were in stable condition at a hospital.
The Air Canada Express CRJ-900 plane, operated by its partner Jazz Aviation, was carrying 72 passengers and four crew members from Montreal, based on a preliminary passenger list that remained subject to confirmation.
The aircraft struck the fire vehicle at a speed of about 40km/h, said flight tracking website Flightradar24.
Photos taken by Reuters after the accident showed visible damage to the nose of the plane, which was tilted upward.
Authorities and emergency agencies did not offer any immediate comments on deaths or injuries.
The US Federal Aviation Administration (FAA) said the airport was expected to remain shut until Monday afternoon.
Flightradar24 said 18 flights had been diverted to other airports, mostly in the New York area, or returned to their point of origin.
Air Canada referred Reuters to Jazz's statement and said it was aware of the incident.
The National Transportation Safety Board and the FAA did not immediately respond to requests for comment.
The Port Authority of New York and New Jersey said the firefighting vehicle was responding to a separate incident when it was struck by the aircraft at runway four.
New York City's emergency notification system said people could expect cancellations, road closures, traffic delays and emergency personnel near the airport.
LaGuardia served more than 30 million annual passengers in 2025, according to the Port Authority of New York and New Jersey, and a wide range of US airlines operate at the airport.
