The airport has warned there will be knock-on delays affecting arrivals and departures as a result.
All flights were suspended earlier – the airport has said some flights were starting to take off but inbound flights have so far been cancelled.
The airport’s managing director Graham Keddie said the aircraft had landed “right at the wrong time” and “stopped right in the wrong place”.
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"A freight air coming in to land just before 6am had a number of burst tyres and had to stop right in the junction of both our runways," Keddie told the BBC.
"We can’t move it in case there’s damage to the under carriage so basically we’ve had to recalculate the mass to see what level of runway we can operate off.
"We’ve managed to get the first wave of aircraft out but unfortunately our inbounds have been cancelled so far and we’re hoping to get some in shortly."
Keddie added that airlines were working to get people booked onto later flights and he advised passengers to come to the airport and check-in as normal, as well as to check with their airlines that the flights were still operating.