Labour leader Phil Goff announced the resignation this afternoon at a hastily called press conference at his Auckland electoral office.
Police are investigating Mr Hughes after the student laid a complaint against him following a late-night drinking session.
Mr Goff said the events of the past few days had made it increasingly clear to Mr Hughes that the controversy around the allegations had made it "impossible for him to carry out his duties".
"In reaching that decision he is adamant that he has committed no offence," Mr Goff said.
"He needs to focus on clearing his name. I agree this is the right decision."
In a statement issued shortly after the announcement, Mr Hughes said his position as an MP had become "untenable" and it was necessary to resign.
"I have done nothing wrong, and I remain confident that the legal process will have the right outcome," he said.
"My immediate focus is on clearing my name. I will continue to co-operate fully with the police inquiry, which will unfortunately need to continue in the glare of publicity."
Mr Hughes said while people are generally thought to be innocent until proven guilty, "it has become clear to me that this doesn't apply in the political arena".
He said he had "enormous respect for the institution of Parliament" and the values of the Labour party.
"I am not prepared to see my party distracted in the lead up to a critical election," he said.
Mr Hughes thanked Mr Goff, deputy Labour leader Annette King, the people of his former electorate, and the Labour party.
The alleged incident that led to Mr Hughes' resignation happened at Ms King's Wellington home, where Mr Hughes boards, after he had been drinking at two bars with a group of students, including the complainant.
The student left the home and is reported to have either flagged down a police car or walked into its path.
It was then he made the complaint.
Mr Goff yesterday stripped Mr Hughes from his roles as education spokesman and chief party whip, pending the outcome of the police inquiry.
The third-term MP had been put on two weeks' leave and reportedly has not stayed at Ms King's home for several days.
Mr Hughes was one of Labour's rising stars, having been promoted to the front bench in February, when he took on the role of education spokesman and rose to eighth on the party list.
He entered Parliament in 2002 when elected MP for Otaki aged 24, making him the youngest MP for the two terms he held the seat.
He had the smallest majority of any MP in the 2005 election, with just 382 votes more than National MP Nathan Guy, before losing the seat to Mr Guy in 2008 by 1354 votes.
Mr Hughes was whip in Helen Clark's government from the age of 25, before becoming statistics minister and associate social development and employment minister four years later. He was also deputy leader of the House.
Mr Goff has been put in a difficult position over his handling of the affair.
In 2009 he attacked Prime Minister John Key for not revealing everything he knew about the sex scandal surrounding Richard Worth, a minister at the time who subsequently resigned from Parliament.
Mr Key stood Dr Worth down as soon as he found out about the allegations surrounding the MP, and yesterday Mr Goff admitted he had been wrong when he demanded full disclosure.
"I think I've learnt one or two things about the complexity of these situations," Mr Goff said.
"I'm going to be the first to admit that I was wrong in the judgment that I made at that time."
Mr Goff yesterday said his caucus had not expressed any concerns and his leadership was not an issue.
Prime Minister John Key's office had no comment on the resignation.
