The 40-year-old was struck by the bus travelling eastbound near the Mound.
Emergency services were called at around 11:30 and the woman was subsequently taken to hospital.
East Coast Buses have confirmed that it was one of their vehicles involved in the incident.
It is understood that the woman sustained a head injury.
The area around the Mound was closed for more than an hour following the accident but has now reopened.
A Police Scotland spokesman said: “Police in Edinburgh responded to Princes Street at around 11.30am on Friday 6th July following a collision involving a bus and a female pedestrian at The Mound.
“The 40-year-old has been taken to the Royal Infirmary of Edinburgh with a suspected head injury, where she continues to be treated.
“Inquiries into the full circumstances of this incident are ongoing and anyone with information is asked to come forward.”
A Spokeswoman for East Coast Buses said: “We can confirm that our vehicle was involved in an incident today and we are supporting Police Scotland with this investigation.”
A spokesman for the Scottish Ambulance Service added: “We received a call at 11:19 hours today to attend an incident on Princes Street in Edinburgh.
“We dispatched a paramedic response unit and one ambulance to the scene. One female patient was transported to the Royal Infirmary of Edinburgh.”
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