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...