Penn secretly interviewed Guzman in October when the fugitive drug kingpin was being hunted by authorities following his jail break in July, according to an article the actor published on Saturday in Rolling Stone magazine, Xinhua reported.
Mexican actress Kate del Castillo, who helped arrange the meetings and purportedly planned to produce a biopic on Guzman, is also under investigation.
According to the daily La Jornada, the organised crime division of Mexico's Attorney General's Office (PGR) "opened a preliminary probe to investigate the US film actor and director Sean Penn and the actress Kate del Castillo... in relation to the crime of concealment, since they were aware that Joaquin 'El Chapo' Guzman was a fugitive from justice and nevertheless met with him without notifying Mexican authorities of the meeting."
The head of the Sinaloa Cartel, who was recaptured on Friday, was keen to have his life story told.
The head of the PGR, Arely Gomez, said after his capture that the contact between Guzman and the filmmakers led officials to the location where he was hiding out.
Despite the incidental help from the filmmakers, however, the PGR plans to question Castillo in the next few days, the daily said, adding she is likely to attest that her actions are protected by laws governing the right of journalists and freedom of information.
Regarding Penn, the daily said, "The PGR can request the cooperation of US authorities" in arranging to interview him as a witness at a Mexican embassy.
Rolling Stone touted the interview via Twitter on Sunday, posting "Read Sean Penn's account of his secret visit with El Chapo, before the drug lord's recapture."
According to transcripts of the interview, El Chapo said that while he tried drugs when he was younger, he hasn't touched them in two decades.
Asked how he got into the illicit drug business, El Chapo said that as a young man of 15 in the small town of Badiguarato, Sinaloa, he found that "the only way to have money to buy food, to survive, was to plant marijuana and at that age I began to grow and sell it."