Just before 11am on Monday, a NSW Fire and Rescue truck was responding to an emergency incident when the collision took place at the intersection of Pitt Street and Eddy Avenue.
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The tram derailed from the tracks due to the impact.
Two firefighters inside the vehicle sustained minor injuries, said a spokesperson for NSW Fire and Rescue.
Several light rail passengers were also treated for minor back injuries, according to NSW Police.
An elderly woman sustained a leg injury during the crash.
A spokesperson for NSW Ambulance said two passengers with injuries were hospitalised at St Vincents and RPA in a stable condition.
Pitt Street is currently closed between Lee Street and Hay Street.
Eddy Avenue is currently closed between Elizabeth Street and George Street.
NSW Police are advising motorists to expect traffic delays, and urging the public to avoid the area.