The motion was rejected by 290 votes to 252 after the Liberal Democrats abstained.
A majority of 38 indicated that some non-Tory MPs backed Prime Minister David Cameron's stance that Hunt need not be referred to independent adviser on ministerial interests Sir Alex Allan.
During the Commons debate, Chris Bryant MP claimed that Hunt deliberately misled parliament in his statements about his handling of the planned BSkyB deal.
Despite calls from Conservative MPs for the claim to be withdrawn, Speaker John Bercow appeared to allow it to stand.
"It is up to the Speaker what he judges to be a point of order," BBC News later quoted Cameron's spokeswoman as saying.
The News Corporation bid for BSkyB was withdrawn by the company in the wake of the phone hacking scandal, after it emerged that journalists at the News of the World had listened to voicemails left on the phone of murdered schoolgirl Milly Dowler.
Hunt last week spoke to the Leveson inquiry into press ethics about his quasi-judicial role in deciding whether or not to refer to the competition commission the News Corporation bid for the part of BSkyB it did not already own.
The minister claimed during his testimony that he was "sympathetic" though not necessarily "supportive" of the bid.
Vince Cable had previously been relieved of the decision after he was recorded telling undercover reporters that he had "declared war" on Rupert Murdoch.