The victim was standing outside the City nightclub in Market Street when she was hit by the bottle thrown from above her.
She was treated for a gash to the head by ambulance staff at the scene following the incident, which took place at 3am on Saturday.
Police said her injuries could have been much worse and along with local councillors urged anyone who could identify the “stupid” culprit to come forward.
Inspector Gary Dickson, from the city centre policing team, said: “This was a highly reckless and dangerous act and the person responsible obviously had no regard for the safety of the pedestrians below.
“Thankfully the woman only sustained fairly minor injuries, however the consequences could have been much more serious.
“Both North Bridge and Market Street would have been busy at the time with people leaving bars and nightclubs, and I would appeal to anyone who may have seen the incident to telephone us immediately.
“Similarly, anyone who thinks they know who the culprit is should get in touch with us immediately.”
Councillor Joanna Mowat, who represents the city centre ward, said the incident could have had “tragic” consequences.
She said: “It’s a stupid and reckless thing to throw anything off a bridge. I have nothing but contempt for people that do things like this and I wish well the poor wonan that was hit and hope she is recovering.
“It’s really stupid behaviour and anyone that sees someone behaving like this should report it to the police because the consequences could be absolutely tragic.”
It was the latest in a series of incidents in recent years where people have been hurt by items thrown off city bridges onto streets below.
In the most serious case, 23-year-old Queen Margaret University student Kate Flannery, from Galway, was hit by a traffic cone thrown off George IV Bridge in November 2006.
In July 2007, Andrew Smith, 30, was ordered to carry out 180 hours’ community service for throwing the cone which struck Ms Flannery, who was lucky not to be left paralysed.
Anyone with information on Saturday’s incident is asked to contact police on 0131-311 3131 or Crimestoppers in confidence on 0800 555 111.