Three ambulances were sent to the scene - only to hampered by heavy traffic on one of the busiest Illuminations nights of the year.
The shunt between the two trams took place on South Promenade at its junction with Barton Avenue at 7.45pm,close to Manchester Square.
One tram had stopped, when it was struck from behind by another tram heading in the same direction.
With thousands of families visiting the lights during the half term holidays, the traffic was queued along the entire stretch of the Promenade and onto Squires Gate Lane.
Paramedics were forced to drive along the tram tracks in order to reach the injured, three transport workers and three members of the public, none of which is believed to be serious.
An ambulance spokesman said: "An emergency rescue operation was put into place. Three ambulances were dispatched and an ambulance officer made his way to the scene.
"When we first got the call our worst fears were that this was a serious incident and we treated it as such. We treated six people at the scene for back and neck injuries and ferried them to hospital in the three ambulances.
"Fortunately the incident was not as serious as first thought. This was a low impact crash."
Police were called to the scene by paramedics, who helped keep traffic flowing throughout the incident, which lasted one hour.
Trams were unable to continue running until the damaged vehicles were removed following clearance from the Railway Investigation Board.