"In a leadership contest of fairytale tax cuts and unworkable pledges, this promise to get a new deal or leave without a deal on October 31 is the most ludicrous of them all", worldwide development minister Stewart said in a statement.
The move comes after a number of high-profile contenders for the Tory leadership said they would be prepared to take the United Kingdom out of the European Union without a deal if no new agreement had been reached by October 31.
Dominic Grieve has said he would not hesitate to bring down the government and resign the Conservative whip if new PM forced through no-deal Brexit without consent of MPs.
Johnson said earlier launching his leadership manifesto that he wanted to agree a withdrawal deal with Brussels, but wanted to keep the option of a no-deal Brexit.
MPs opposed the motion by 309 votes to 298.
Labour used an opposition day to table a controversial business motion that sought to "put power back in the hands of Parliament" and pave the way for another vote in June that, if passed, would block a no deal.
MP's have rejected a cross-party motion to stop any future Prime Minister pushing through a no-deal Brexit.
"We will simply not get a result if we give the impression that we want to go on kicking the can down the road and yet more delay", Johnson said.
"That's why we are taking this latest measure to end the uncertainty and protect communities across the country".
Mr Johnson has kept a low profile in the race to succeed Theresa May so far, his only significant intervention being a pledge - immediately criticised by his rivals - to cut income tax bills for people earning more than £50,000 a year.
Questioned about his comment that Muslim women in full face veils looked like "letter boxes", he said voters were alienated by politicians using "bureaucratic platitudes".
Shadow Brexit secretary Sir Keir Starmer said Labour will use its opposition time on Wednesday to try to give control of Parliament's agenda to MPs on Tuesday June 25.
"It is a first and limited step to ensure parliament can not be locked out of the Brexit process over the coming weeks and months", he said.
And former Tory MP Nick Boles, who is now an independent, said he would be flying back from a trip overseas to back the motion.
Government sources said the motion would set an "uncomfortable and troubling precedent" and were clear that Tory MPs would be whipped to vote against it.