There were no passengers on board at the time of the incident, the airport has confirmed.
One witness tweeted: “The Astral 747 we saw has come off the runway nose gear embedded in the grass while backtracking.”
A spokesperson from Doncaster Sheffield Airport (DSA) said: “We can confirm that the runway at DSA is temporarily closed due to a 747 freight aircraft requiring operational support.
“There were no passengers on board at the time of the incident, and there were no injuries to colleagues or crew.
“The freight on board the aircraft may be offloaded to aid recovery.
“The fire team attended to assess the situation, have confirmed that the aircraft is safe, and have now returned to the station.
The spokesperson added: “At this time it is unclear how quickly the runway can reopen.
“Passengers travelling to Katowice and Gdansk this evening should keep in touch with their airline.
“Updates will be provided over the next few hours as the situation becomes clearer.”
Doncaster Sheffield Airport later confirmed that the runway would remain closed until Wednesday, when departures will operate as planned.
Astral Aviation is a cargo airline based in Nairobi, Kenya.
The firm was established in 2000.
Astral operates cargo flights to regional destinations in Africa and to Liege in Belgium.
Doncaster Sheffield Airport and London Stansted Airport are among its UK destinations.