No one was injured in the accident at West Maitland Street at 7.45am, but it brought traffic chaos to the city centre at rush hour.
The tram was not derailed and Transport for Edinburgh, which operates both buses and tams for Edinburgh City Council, removed the vehicle.
Police said both bus and tram were travelling towards the city centre and traffic warnings were issued.
Dalry Road and Haymarket Terrace was affected and the road was reported blocked southbound at Palmerston Place at West Maitland Street.
A Police Scotland spokeswoman said the area was "gridlocked" at 9am.
She said diversions were in place and added: "the situation is ongoing".
Edinburgh Trams confirmed on their Twitter that services were running as normal.
It is the latest incident to hit the trams in the three months since the troubled £776 million system started running, after balloons caught in an overhead line closed the entire system and the same happened after a tram broke down at Haymarket.
A teenager was also hit by a tram in June but was uninjured.