John Mann MP said he wanted a "full inquiry" after the club voted to endorse Israel Apartheid Week.
Club co-chairman Alex Chalmers resigned after the vote and said many members had "some kind of problem with Jews".
Labour Students is now investigating the allegations at the club, which said it would fully co-operate.
Mr Chalmers, an Oriel College undergraduate, posted on Facebook that certain members' attitudes at the Oxford University Labour Club (OULC) were becoming "poisonous".
He said "a large proportion of both OULC and the Student Left in Oxford more generally have some kind of problem with Jews".
He said the decision to endorse Israel Apartheid Week illustrated the "uneven and insincere" attitude of some members "when it comes to liberation".
According to its website, Israel Apartheid Week takes place across 150 universities and cities and "aims to raise awareness about Israel's ongoing settler-colonial project and apartheid policies over the Palestinian people".
Oxford University Labour Club said in a statement: "We are horrified at and whole-heartedly condemn anti-Semitic behaviour in all its forms."
It said the allegations would be "dealt with swiftly and lastingly".
Labour Students, the national youth body of the political party, said it was "deeply troubled" by the reports of anti-Semitism and had launched an immediate investigation.
John Mann, Labour MP for Bassetlaw in Nottinghamshire, said he had written to the party asking for an investigation.
He added: "It is hugely embarrassing for the Labour Party. This is something Jeremy Corbyn should personally look into."
A spokesman for the Labour Party said it supported the investigation.
A statement from Oxford University Jewish Society said the group was "saddened by the anti-Semitic reports".
It added: "We are, however, unsurprised by this news.
"It is not the first time that Oxford JSoc has had to deal with anti-Semitic incidents within the Student Left and it will not be the last."
Oxford University said students were encouraged to officially report harassment to the university authorities.
A Labour MP has called for the Oxford University branch of the party to be suspended over allegations of anti-Semitism by its members.