Staff planned the walk out with five other colleges over a long-running pay dispute. But an agreement to hold talks with the Advisory, Conciliation & Arbitration Service (ACAS) this month saw Askham staff step back from the brink.
The five other colleges involved in the dispute - Doncaster College, Rotherham College, Leeds College of Art & Design, Greenwich Community College and Suffolk New College in Ipswich - carried out strike action on 29 September.
The dispute concerns the colleges' failure to implement a pay recommendation from 2004 which would see lecturers earning up to £4,500 more. A University & College Union (UCU) representative said: "A national pay framework was agreed in 2004 and it is wrong for colleges to still be holding out on paying that in 2009."
A statement issued by Askham Bryan College said: "The strike action planned was postponed due to the progress that has been made in discussions with the UCU. "
The UCU also identified that Myerscough College had failed to implement the pay recommendation but no strikes are planned at this stage. Pershore College is in talks with the UCU.