More than 160 Unite union members employed by Vanderlande Industries last month voted to strike from 8-10 April over pay.
However, Unite on Monday (4 April) confirmed the action had been postponed to allow members to vote on a new pay deal put forward by Vanderlande.
If members reject the deal, Unite said the strike action would be rescheduled for a later date.
Airlines that could be affected if a strike goes ahead, said Unite, include British Airways, KLM, Air France and Lufthansa.
Vanderlande’s workers at Heathrow are responsible for operating and maintaining the baggage systems across all five terminals at the west London airport.
Unite regional officer Lindsey Olliver said: “During negotiations last week, held under the auspices of the conciliation service ACAS, Vanderlande put forward a new offer.
“Over the next two weeks, Unite will be balloting our members on whether it meets their aspirations.”
A Heathrow spokesperson said: “We are pleased to hear that industrial action planned for this weekend has been postponed. This involved colleagues from Vanderlande Industries who operate at Heathrow.
"While their discussions remain ongoing with their employer we will continue to liaise with airport partners on contingency plans for the airport’s operations, should the action be rescheduled at a future date.”
TTG has also approached Vanderlande for comment.