The move comes to give the union time to consult with members over an improved pay deal put forward by airport bosses.
Workers at the airport were set to walk out for three days following a dispute over pay – which saw a ballot return of 93% vote in favour of industrial action.
Joe Wheatley, GMB negotiator, said: "Following a number of commitments put forward by Leeds Bradford bosses to improve pay, we now need to fully consult with our members working in security at the airport.
"GMB’s strike committee has agreed to suspend next week’s planned strike action to give us the facility, time and space to consider the new, improved offer with our members."
A Leeds Bradford spokesperson said: “Our colleagues are at the forefront of LBA and we recognise their hard work and significant contributions. We are pleased to have worked closely and constructively with GMB to make progress towards an agreement.
"We’re committed to providing a quality service for our passengers and today is a positive step towards a conclusive agreement with the union and our staff."