The Cabinet Office said the election for the vacant seat, planned for 4 May, would now take place on 8 June as part of the nationwide polling day.
MPs will be asked to formally overturn the writ for the poll.
The proposed by-election would have created the anomaly of taking place after Parliament had been dissolved.
The by-election was caused by the death of long-serving Labour MP Sir Gerald Kaufman in February.
Commons Leader David Lidington told MPs there was no statutory provision allowing for the cancellation of a by-election when a general election was in progress.
But he said a precedent was set in a similar situation in 1923, when a by-election writ was regarded as having been superseded.
The Commons vote would enable Manchester's acting returning officer Joanne Roney to cancel the by-election.

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Currie's anticipated appointment was confirmed at Shamrock Park on Monday evening as his five-year stint as Ards manager came to an end.
The Portadown native, 44, emerged as the club's preferred candidate over the past week.
Currie, who has been handed an 18-month contract, takes over a side that are 13 points adrift at the bottom of the Premiership table.
Portadown started the season with a 12-point deduction for making irregular payments to players and were also handed a number of fines, in addition to being prevented from signing players on professional deals this season.
Despite the team's predicament, the new manager described his appointment as the "pinnacle for me".
"I was in a strong position and a secure job at Ards, but my heart led me here. The lure of coming home and managing my hometown club was too strong," said Currie at the news conference confirming his appointment.
"We're going through a tough time at the moment but I want to bring a smile back to this club.
"Our first priority is doing our utmost to stay in the league and we want to give it a real rattle."
Currie has arrived from Ards with long-term assistant Jay Willis while Trevor Williamson will remain part of the backroom team.
One of the new manager's first acts has been to recall former Linfield striker Mark McAllister to the first-team squad.
Back in September, then manager Pat McGibbon told McAllister that he was no longer part of the club's plans.
However, Currie believes the striker can be an asset to the squad.
"He's looking forward to playing and getting himself fit," said the new manager.
"We've got some good defenders and some good midfielders but I think we need to inject a bit of pace into the last third of the pitch."
A statement from Ards on Monday night said that the North Down club had received "an amount of compensation from Portadown for Currie's services" but that there would be "further discussions between the two clubs".
The Ards statement added that first-team coach John Bailie will act as their caretaker manager as the club decides how to go about appointing a successor to Currie.
Vinny Arkins stepped aside as interim Ports boss last Thursday, having been in caretaker charge of the crisis club since previous manager McGibbon resigned in mid October.
Arkins was not in contention to succeed McGibbon as he does not hold a Uefa A coaching licence.
After playing 19 games in the Irish Premiership campaign, Portadown are cut adrift at the bottom of the table on minus one points, which leaves them 13 points behind 11th-placed Carrick Rangers.
A by-election for the Manchester Gorton constituency is set to be cancelled after the House of Commons backed a June general election.
[NEXT_CONCEPT]
Niall Currie has been unveiled as the new manager of Portadown.