The incident happened on Coates Place, but the severity is still unknown.
Traffic is thought to be moving in the area.
Passengers were being held on the damaged tram while engineers assessed the damage.
Andrew Forsyth, a partner in Coates Place design firm Darling Forsyth, said: "I didn't actually see the collision but I heard an almighty bang and then we saw the damage to the tram.
"I don't know who is to blame but it is a really narrow bit of road just there.
"You can see that the front door of the tram has been badly damaged. I imagine the trams will be off for a good while."
A spokeswoman for Edinburgh Trams said:“At approximately 12.25 today there was a minor road traffic collision where a lorry came into contact with a tram at Atholl Place. We are still operating at full route, however we ask that customers bear with us as we resume a regular frequency service.”
For the latest breaking news and incidents around Edinburgh - join our new Facebook group here.