More than 1,000 drivers and engineers were set to stage the walkout on Bank Holiday Monday in a dispute over rosters.
It was supposed to be the second day of strike action after Unite members at Tower Transit took action on Friday.
It said it decided to suspend Monday's industrial action after "solid support" for Friday's protest.
A spokesperson said it wanted to give the company time to "reflect and respond".
Transport for London said Tower Transit operated less than 5% of the bus network.
A planned bus drivers' strike which threatened to disrupt Notting Hill Carnival has been called off.