The Fire and Rescue NSW crew were on their way to another incident when the crash occurred.
"NSW Ambulance paramedics were initially called to treat five patients," NSW Ambulance inspector Ben Saywell said.
"Three people were assessed by paramedics and didn't require any further treatment, while two people were taken to hospital.
"This occurred in a really busy part of the CBD with a lot of pedestrians, so we're thankful that no one was seriously injured."
The force of the crash was so strong that the tram came off the tracks.
Multiple traffic diversions are in place around the area.
Pitt St has been blocked in both directions, while there is also no access to Eddy Ave from Elizabeth St.
Light rail services between Central and Circular Quay are not running.
More to come.