MEXICO CITY—Mexico’s finance minister bought a home from a prominent government contractor who is at the center of influence-peddling allegations roiling President Enrique Peña Nieto ’s administration, documents viewed by The Wall Street Journal show.

Property records show that the minister, Luis Videgaray, widely seen as the driving force behind Mexico’s recent economic overhauls, bought the house in an exclusive golf resort outside the picturesque town of Malinalco, in the central State of Mexico, from Bienes Raíces H&G SA.

The firm, commercial records show, is owned by Juan Armando Hinojosa, whose companies have won hundreds of millions of dollars’ worth of public-works projects during Mr. Peña Nieto’s time as governor of the State of Mexico and during his current administration.

Mr. Videgaray isn’t accused of an illegal act. But the transaction adds to the appearance of conflicts of interest that have damaged Mr. Peña Nieto’s credibility and popularity after he came to office promising a break from the clubby practices of his ruling Institutional Revolutionary Party’s past. It also is a fresh example of the extensive business and personal links between the contractor and senior government officials.

Mr. Videgaray, in written response to questions from the Journal, said that he bought the house from Mr. Hinojosa in October 2012, a few months before Mr. Peña Nieto’s administration took office on Dec. 1. By then, Mr. Videgaray was widely tipped as the next finance minister.

“There was no conflict of interest. I did the deal when I was not holding public office, and the deal was within market parameters,” Mr. Videgaray said.

The transaction was unusual in that Mr. Videgaray also took out a mortgage with Mr. Hinojosa’s small firm rather than a financial institution, borrowing some $532,000, records show. For financial reasons, Mr. Videgaray said, he later paid off the mortgage in full.

Influence peddling allegations have exploded in Mexico since November, when a team of Mexican investigative journalists revealed that a Hinojosa-owned company built and held the title to a presidential family mansion in Mexico City.

News of the home—whose ownership Mr. Peña Nieto hadn’t disclosed publicly—led to opposition calls for a congressional probe.

That development, along with a public outcry over 43 college students abducted by local police in southern Mexico and allegedly handed to a drug gang to be killed, has sparked a political crisis for the president.

His 39% approval rating is the lowest for a Mexican leader in nearly two decades, according to a recent Reforma newspaper poll.

The president’s office has denied allegations of impropriety. It said first lady Angélica Rivera was buying the house from Mr. Hinojosa with money from her long acting career, and said the couple keep their assets separate.

Mr. Hinojosa declined to comment about either transaction and hasn’t made any public remarks on the matters.

The U.S.-educated Videgaray is seen by many as the architect of the administration’s successful economic overhaul, including opening Mexico’s energy market to private firms. He was named global finance minister of 2014 by two British magazines, Euromoney and the Banker, and the U.S.’s Foreign Policy magazine named him one of its 100 leading global thinkers.

But the former investment banker is facing rising headwinds at home, amid tepid economic growth and a sharp drop in prices for Mexico’s oil exports, which represent about one-third of government revenue.

Mr. Hinojosa, 58 years old, rose to prominence as a businessman during the same period Mr. Peña Nieto, 48, did as a politician. And much of the time that Mr. Peña Nieto was governor of Mexico’s most populous state from 2005 to 2011, Mr. Videgaray, 46, was his state finance chief.

Mr. Hinojosa, whose companies are based in Toluca, the State of Mexico’s capital, was widely seen as close to both Mr. Peña Nieto and to Mr. Videgaray. For example, Mr. Peña Nieto and his wife attended the funeral of Mr. Hinojosa’s son after he died in a 2012 helicopter accident.

Mr. Videgaray said he has known Mr. Hinojosa for longer than a decade. “I have a social relationship and friendship with him and his family,” he said.

Amid those personal contacts, Mr. Hinojosa’s success in winning government contracts has raised eyebrows among many Mexicans.

Units of Mr. Hinojosa’s holding company Grupo Higa SA earned major contracts during the time Mr. Peña Nieto was governor, including a $500 million deal in 2009 to build a hospital in the city of Zumpango and several highways.

Since Mr. Peña Nieto became president, companies owned by Mr. Hinojosa have won a share of a $3.4 billion contract to build an aqueduct to supply water to Monterrey, several federal highway projects, and a no-bid contract to revamp the presidential hangar at the Mexico City airport, records show. Mr. Peña Nieto’s office rejected any suggestions of favoritism in the bidding process.

A Hinojosa company was also part of a consortium led by Chinese firms that won a $3.7 billion contract for a high-speed train, which was abruptly canceled by the government in November days after it was awarded and days before the report emerged over the president’s home. The government said it was responding to complaints from rival bidders who said they had insufficient time to bid.

In 2012, when Mr. Videgaray was the head of Mr. Peña Nieto’s presidential campaign, his party contracted a Hinojosa-owned aircraft unit to provide air transportation for the candidate, according to public records. A luxury home also owned by Mr. Hinojosa was used as an office during Mr. Peña Nieto’s time as a candidate, when Mr. Videgaray was campaign chief, and after the candidate became president-elect.

The Malinalco house, registered at some 9,200 square feet, appears in Mr. Videgaray’s disclosure of assets, which federal officials in Mexico are required to submit annually.

The president’s office said Mr. Peña Nieto didn’t disclose details of the Mexico City mansion because his wife isn’t a public servant.

What wasn’t apparent until now was the house’s seller, which property records show to be Bienes Raíces H&G. Commercial records in Mexico City say the company is 96% owned by Mr. Hinojosa.

Mr. Videgaray bought the house for 7.5 million pesos, or about $581,000 at the time, records show, with a mortgage with H&G to be paid over 18 years. The mortgage wasn’t disclosed in Mr. Videgaray’s asset disclosure.

Mr. Videgaray said he didn’t disclose the loan because the government electronic form didn’t allow him to specify that it was a nonbank loan. He attached an explanatory note to his disclosure saying he had a nonbank loan. The note, labeled for internal government use and not made available to the public, was seen by The Wall Street Journal.

By Jan. 31, 2014, a few months into office, Mr. Videgaray paid off the entire debt with a single payment, records show. “For financial reasons, I decided to prepay the loan as fast as I could.”

Homes in the development, Club de Golf Malinalco, now sell for between $850,000 to $1.2 million, said a saleswoman at Sotheby’s International Realty. The residential development includes an 18-hole golf course and a helicopter landing site.