Amina Ali, from London, was named on Saturday as the "overwhelming choice" from an all-women shortlist.
The seat is held by the Respect Party's George Galloway, who took it from Labour in a by-election in 2012.
Mr Galloway said the "real reason" for her withdrawal was the the "war inside Bradford West Labour Party".
Len Tingle, BBC Look North's political editor, said the news of the withdrawal was "deeply embarrassing" for Labour.
Ms Ali, a British-Somali, said: "I am the mother of two children and, despite my best efforts to make arrangements to bring them to Bradford for the next 70 days, particularly as one of them is doing her GCSEs, this would have caused massive disruption at a critical time.
"I would not be able to do justice to the members of Bradford West CLP [constituency Labour Party] and the people of Bradford.
"Bradford West needs a candidate who is going to live in Bradford and be involved in the campaign for every moment of every day."
A Labour Party statement said: "As Amina Ali has made clear, she found it impossible to balance her family commitments with the commitment needed to be a parliamentary candidate.
"We understand and sympathise with her position."
Mr Galloway tweeted: "Bradford New Labour. A supernova shambles..." after Ms Ali's withdrawal was announced.
"Didn't she think it through before she put her name forward? Of course she did, and no-one's going to be taken in by that," he added in a statement.
Ms Ali, a councillor in Tower Hamlets, east London, worked as a researcher and journalist for the BBC before embarking on her current career as a legal adviser, a Labour Party spokesman said.
Speaking on Saturday, she said: "I'm delighted to have been given the backing of Bradford West members and will give this campaign everything I have."
Mr Galloway, who was expelled by Labour in 2003, won the seat in 2012 with a 10,140 majority - which he claimed was the "most sensational victory" in by-election history.
At the 2010 general election, Labour's Marsha Singh won the seat but he later resigned on health grounds. Mr Singh died in 2012.