Chuka Umunna, who announced his leadership bid just three days ago, blamed the "added level of pressure that comes with being a leadership candidate."
"I have not found it to be a comfortable experience," Umunna, 36, said in a statement. "Most importantly, I continued to have very real concerns and worry about this bid's impact on those close to me."
Umunna's withdrawal casts a shadow on the Labour Party, already in disarray after its defeat in Britain's general election last week. Miliband stepped down after his party lost almost all of its seats in Scotland to the separatist Scottish National Party and ran well behind the winning Conservatives elsewhere.
Umunna, a lawyer, is the party's business spokesman. A relative newcomer, he has risen quickly in the party's ranks since he was first elected to Parliament five years ago.
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Umunna was one of five Labour politicians who threw their hat in the ring in the past few days. One of them, Yvette Cooper, said on Twitter it was a "real shame" that Umunna has had to quit and "had pressure put on friends and family."
The last Labour government was led by Gordon Brown from 2007 to 2010.