The Fire Department of New York says 10 other people have also received medical treatment following the collision at about 6:15 am today at an intersection in the Flushing neighborhood.
One of the buses also hit a building. Firefighters have extinguished a blaze there.
A photo tweeted by the NYPD's 109th Precinct shows the buses side-by-side facing opposite directions, with the city bus slightly tilted to one side.
A Fire Department photo on Twitter shows firefighters responding outside the building.
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