Organisers said restrictions imposed by the Civil Aviation Authority (CAA) after the crash at Shoreham Airshow would have "seriously limited" some of the flying displays.
The event has been rescheduled for Saturday 28 May 2016 and tickets already issued will remain valid.
The show would have been the first to be held in the area since 1989.
Chris Petty, from organisers Skylive, said the decision had not been taken lightly.
"We had put together an excellent programme of events but clearly the tragedy at Shoreham has forced us to consider very carefully whether it would be right to go ahead.
"The restrictions announced by the CAA...would have seriously limited the flying displays of the jet aircraft scheduled to take part - including the Avro Vulcan and the aircraft from the Swedish Air Force Historic Flight - it would have significantly reduced the quality of the central element of the event."
A spokesman for Durham Tees Valley Airport said it believed the decision to postpone was the right one.
An air show due to take place at Durham Tees Valley Airport on Saturday has been postponed.