The Los Angeles Times reported four banners appeared in different parts of the city on Tuesday warning the 24-year-old singer to cancel his concert on Oct. 14.
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The banners read the show would be "his last" due to the singer's "disrespect and loose tongue."
The Associated Press reported one man was arrested for his involvement in the threats. The mayor of Tijuana, Montserrat Caballero, pointed out that depending on what investigators find, the concert may or may not be authorized.
Peso Pluma, who is known to praise Mexican drug kingpin Joaquin "El Chapo" Guzman in his songs, made history Tuesday by becoming the first Mexican star to perform at the MTV Video Music Awards.
Caballero indicated that it is unknown if the banners were placed by members of organized crime who were offended by any of the musical themes or by a citizen who doesn't like Peso Pluma's music.
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"Singers are definitely the ones who make the mark by advocating crime and they know the risk they run," he added.
The singer has not commented on the threats and has postponed some of his upcoming U.S. concerts.
The Associated Press contributed to this report.