Flights were suspended for two hours at Birmingham Airport after a plane skidded off the runway.
The airport said the Monarch-chartered flight ZB467, from Nice in France, skidded off the runway at 13:10 BST.
The airport said the Boeing 737 was operated by Lithuanian firm Aurela Airlines.
Monarch said it was the same 737 which left 150 people stranded in Tenerife last month when a door broke. It said it had suspended the use of Aurela.
None of the 135 passengers involved in Friday's incident were injured.
Monarch said the plane was being taxied to the terminal in Birmingham when "one set of wheels left the taxi way bringing the aircraft to a stop".
Passengers said there had first appeared to be problems with the aircraft's brakes as it was being taxied in Nice, and described it as a "very old plane".
All flights to and from the airport were immediately suspended after the incident. The runway reopened at about 15:10 BST.
The airport warned some departures were still delayed.
Tim Witcherley, from Warwickshire, who had been on the flight, said there had first been a problem with the aircraft when it took off in Nice.
He said: "When we were being taxied on the runway, the plane turned and there was a juddering noise, as if the brakes had locked up, like you get on a car.
"Then it took off and we had an uneventful journey until we got back to Birmingham. Again, it was when we turned right that the same juddering started, the plane tilted and we ended up on the grass.
"There was no shouting, no panicking - people were just laughing. It was all very British."
Another passenger, Ian Smith, said it was the "oldest plane" he had "ever flown on".
He added: "We landed on the runway fine but then something went wrong with taxiing.
"It [might have been] going too fast... and we slid on to the grass. We couldn't really see a lot, we weren't actually too far from the perimeter fence and trees.
"It's only after that you think it could've been a lot worse. We're all fine and disembarked normally."
Faulty door hatch
Last month, about 150 passengers were left stranded in Tenerife for two days after the same Aurela Airlines plane, again chartered by Monarch, had technical problems.
The customers were asked to get off the plane, which was due to fly back to Birmingham Airport, after problems with a faulty door hatch.
BBC transport correspondent Richard Westcott said it was "very common" for companies like Monarch to hire in planes from other airlines during busy periods.
Monarch said it was working with the airport to investigate what happened in Friday's incident.
It said that as a "standard precaution", emergency services were called to the aircraft.
Monarch apologised to all the passengers and said it was "offering them all possible assistance".
Eyewitnesses said no emergency chutes were deployed and luggage was soon being taken off the aircraft.
East Midlands Airport said seven flights bound for Birmingham Airport had been diverted there.
Airport chief executive Paul Kehoe said the aircraft had now been towed away to a siding and was no longer blocking the runway or any taxiways.
He said he did not believe there was much damage to the aircraft but that engineers and the Air Accident Investigation Branch would be examining it.
West Midlands Ambulance Service said it had attended the scene and all passengers had "safely disembarked from the aircraft".
A spokesman said no passengers were treated at the scene or taken to hospital.