Voters in Manchester Gorton face waiting an extra month to elect their new MP, with May's by-election likely to be scrapped.
Commons Leader David Lidington said he expected the planned May 4 vote not to take place.
Under the timetable for Theresa May's snap general election, Parliament will be dissolved on May 3 - meaning there would be no House of Commons for an MP to be elected to.
Downing Street had originally indicated that it expected the by-election, triggered by the death of Labour veteran Sir Gerald Kaufman, to go ahead.
But Mr Lidington said he expected the returning officer in Manchester Gorton to cancel the poll, with the general election expected on June 8.
Manchester's returning officer Joanne Roney said she was in discussions with the Government and Electoral Commission about the situation.
Mr Lidington told MPs: "There is no statutory provision that provides for the cancellation of a by-election when a general election is in progress.
"It is up to the judgment of the acting returning officer, whom one might expect to regard the by-election writ as having been superseded.
"This was the course of action taken by the acting returning officer in the one precedent that I found, which is dating back to November 1923."
Ms Roney said: "We are seeking advice in discussion with the Government and Electoral Commission and will confirm arrangements for the Manchester Gorton constituency as soon as possible."
In Gorton, voters voiced their opinions on the news.
Glenda Breame, 59, said: "It's Parliament arguing about it now, I think they're dragging it out.
"I think they'd get the same result in both elections anyway."
Saima Choudry, 38, said: "I think they should just go ahead with it and elect a member of parliament.
"They need to get on with it now."
One man, who did not want to be named, said he would not vote in a by-election or a general election.
He said: "They are not going to help me so you just have to look after yourself."
Lorna Scott, 50, who works in Gorton Market, said: "I wouldn't like Theresa May's job.
"It all seems very chaotic at the moment so this doesn't surprise me."