The incident happened just after 10.30am and it understood the large Scania lorry hit the bridge before teetering to its left side eventually coming to stop against a nearby wall.
As a result the southbound carriageway heading to the Old Dalkeith Road remains blocked.
Fire and police are on scene and the road is expected to be closed for some time.
The driver is soon to be taken to the nearby Royal Infirmary Edinburgh by paramedics.
Specialist engineers have also been deployed by Network Rail to check the safety of the bridge structure.