All flights were grounded for around three hours on Friday after the Vienna-bound Laudamotion aircraft suffered suspected engine problems on the runway.
Passenger Thomas Steer said after around 15 seconds of acceleration there was a "big bang on the side of the aircraft which skidded to a stop" shortly after 8pm.
The estate agent, 24, from Essex, said: "It was scary. And then staff shouting 'evacuate evacuate'.
"My friend opened the emergency exit and we slid down the slides, a few old people fell over and the fire brigade treated them.
"No-one was seriously injured, just minor things."
An airport spokesman said it had received reports that eight people suffered minor injuries in the incident.
The Air Accidents Investigation Branch said it was sending a team to investigate
Shortly before 11pm, Stansted tweeted "Our runway has now re-opened and is fully operational.
"We are extremely sorry for the disruption caused by the incident but our first priority is always the safety of the passengers and staff."
Images posted to social media by delayed passengers showed several people standing on grass by the runway as emergency service crews and flashing lights surrounded the plane.
Flights to Stansted were diverted to other airports during the disruption.
Airline Laudamotion tweeted: "The crew of OE flight from Stansted to Vienna (1.3.) decided to abort the take off due to engine issues and to disembark the passengers on the runway as a precautionary measure.
"Passengers were transferred to the terminal by bus and will be re-accommodated onto a replacement flight."