Emergency services were called to the accident at the roundabout on Ocean Drive, close to the Holiday Inn Express, at about 1:15pm.
A spokesman for the force said: “There’s been a collision involving a car and a female cyclist at Ocean Drive.
“The woman has lower back injuries and is being assessed by the ambulance service.”
The spokesman added that her injuries are not believed to be life threatening.
The car driver stopped at the scene.
Lothian Buses had also tweeted to alert passengers of some diversions for services using the Ocean Drive route.
However their latest tweet says the diversion has now ended.
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