Ferry Road was closed between Newhaven Road and Craighall Road following a crash between a number 14 Lothian Bus and a private hire coach.
It is understood a number of other passengers were treated at the scene according to the Scots Ambulance Service.
A spokesperson said: “We received a call at 0858am today to attend an road traffic collision on Ferry Road in Edinburgh.
“We dispatched two ambulances, a paramedic response unit, our special operations team and a manager to the scene.
“One female patient was transported to the Royal Infirmary of Edinburgh.”
It is understood both the female passenger and the male driver are being treated for leg injuries.
An image shared on social media shows a number 14 Lothian Bus and a coach from Edinburgh Coachlines involved in the incident.
A spokesperson from Lothian said: “We can confirm that one of our vehicles was involved in a collision this morning and we are cooperating fully with Police Scotland in their ongoing investigation.
“In the meantime, our thoughts are with all those affected by the incident.”
Edinburgh Coachlines onfirmed that their vehicle was involved in a private hire.
A number of passengers on the Lothian service are thought to have sustained injuries.
They also confirmed an emergency response team was on hand to liase with officers.
Local resident Barry Russell, whose flat overlooks the crash scene, said: “I heard the bang and went to see what had happened and saw the damage to the coach and the bus.
“There appeared to be one woman injured on the bus, I’m not sure if she was thrown forward in the collisiom, but she was taken away by the ambulance.
“The bus and the coach are still therre now and so are police and fire.
The road is closed and looks like it will be for some time.”
An eyewitness travelling behind the bus involved in the incident said: “I was on the bus behind. Just heard the noise and seen the aftermath once we jumped off to see what had happened.
“Emergency services were very quick to respond”
A Police Scotland spokeswoman said: “One male taken to hospital and a female as well, both with potentially serious injuries.
“The Lothian bus was removed at 10.31.”