The crash occurred at the North-East corner of the University’s Old College Quad at around 6pm.
“I was told that no one had been injured,” said one witness to the aftermath of the crash.
“It was quite a big drone, so that was lucky,” he added.
A spokesperson for the University of Edinburgh said: “An incident involving a drone occurred in our Old College Quad on Wednesday evening. Nobody was injured and no buildings were damaged. We are liaising with the production company on the matter.”
A representative for the Fast and Furious 9 production company declined to comment.
A member of university staff said he witnessed the aftermath of the crash as he came out of a meeting at 7.20pm.
"It must have happened at roughly 6pm," he said.
"The crash site was in the north-east corner of the Quad. I was told that no one had been injured. It was a big drone, so that was lucky."
He added: "I was told that the police had attended but I did not see any police there at 7.20. I don't know the time of the crash but when I went into my meeting at about 5.50 pm they were carrying out filming and I was told that they planned to stop at 6 pm, so that suggests a time-window for when the crash took place."
Police Scotland failed to respond to requests for comment.
Fast and Furious 9 is currently being filmed at locations throughout the city.
The Hollywood blockbuster, starring Vin Diesel, Michelle Rodriguez, Jordana Brewster, Tyrese Gibson and Chris "Ludacris" Bridges, is due out next year.
A total of 52 roads will be closed in Edinburgh city centre for filming throughout September. A full list of road closures is available here.
The University of Edinburgh Old College Quad sits outside the A-listed Old College building, in the centre of the university campus.
It is popular with film crews, and other productions with scenes shot there include Lone Scherfig's One Day, released in 2011.