Raul Diez Canseco strongly denied wrongdoing on Monday and said in a resignation speech to reporters that the allegations against him were designed to destabilise the government.
"In the last few days I have been the object of a media campaign full of half-truths that has gone beyond all the boundaries of ethics," Diez Canseco said.
He said he was quitting "with dignity, and my head held high." He was replaced by his deputy, Alfredo Ferrero, who was sworn in soon after Diez Canseco quit.
Last week, opposition newspaper Correo accused Diez Canseco of hiring his alleged girlfriend for a job it said she was not qualified for, and getting two of her cousins well-paid jobs. It also said Diez Canseco had favoured her father's company by signing a tax exemption law.
Diez Canseco has denied the woman is his girlfriend and any favouritism toward her family.
"In the last few days I have been the object of a media campaign full of half-truths that has gone beyond all the boundaries of ethics"
Raul Diez Canseco, former trade minister
He said he would be quizzed by a congressional commission on Tuesday in order to "establish the truth."
Although his resignation as tourism and foreign trade minister was irrevocable, Diez Canseco said he was staying on as first vice president.
That means he steps in for Peruvian President Alejandro Toledo if he is out of the country, and would take over if Toledo quit, died or was sacked.
The former minister - a businessman who helped bring to Peru the KFC and Pizza Hut chains, was already in trouble with lawmakers for pulling Peru out of the G21 group of nations that sprang up at world trade talks in Cancun, apparently without consulting Toledo.
But the latest scandal caused even lawmakers from Toledo's Peru Posible party to demand that he go.
"The majority of the parliamentary party agree that he should resign," congressman Luis Flores Vasquez said.