South Yorkshire Aircraft Museum in Dakota Way was due to host its open cockpit weekend on July 15 and 16.
But bosses have announced that the event has had to be shelved.
A spokesman said: “It is with great regret that we must inform you of our decision to cancel next weekend’s open cockpit event.
"This is certainly not a decision we have taken lightly however due to staff illness and unforeseen absences we will be left short of the number of staff required to supervise the event.
"Our open cockpit weekend in October is still planned to go ahead, and if possible we will try to rearrange the July event in a few weeks time.
"Sorry for any disappointment or inconvenience caused.”
The museum, on the site of the former Doncaster Airport, was previously known as Aeroventure.