A Mexican government official confirmed the investigation to CNN.
Del Castillo, a dual citizen of Mexico and the United States, has not been charged with any crime and so far has only been called to give a statement to investigators, Attorney General Arely Gomez told El Universal
The two-pronged investigation -- into the actress's links to drug lord Joaquin "El Chapo" Guzman and into the finances of her boutique tequila brand, Honor Del Castillo -- will determine if drug money went to her business.
There are indications that El Chapo provided illicit funds for del Castillo's tequila business, Gomez told the newspaper, but the links have not been proved.
"Even where there are indications, we need legal certainty," Gomez told El Universal.
Investigators are looking into communications between the actress, Guzman and his lawyer that included comments like "we're in business" and "we're in this together," Gomez said.
Secret meeting with the fugitive
Guzman, the leader of the powerful Sinaloa drug cartel, is behind bars. He was arrested this month after an escape from a maximum-security prison that embarrassed the Mexican government.
But before El Chapo was recaptured, he had a secret meeting with del Castillo and actor Sean Penn in a Mexican jungle. Mexican authorities later said that they were tracking the two actors and that their meeting with the drug capo ultimately led to his capture.
Most of the attention after Guzman's arrest has been on Penn's role and the article he penned for Rolling Stone magazine about his interview with the fugitive kingpin.
But it is del Castillo, who brokered the meeting
, who is wanted for questioning by Mexican investigators.
Penn, the attorney general told El Universal, is not being investigated by Mexican authorities.
Del Castillo has been mostly silent since Guzman's arrest, but she recently thanked her supporters on Twitter.
"Not surprisingly, many have chosen to make up items they think will make good stories and that aren't truthful. I look forward to sharing my story with you," the actress said.
CNN has reached out to del Castillo for comment.
Investigation focused on tequila, not movies
Part of the reason for the meeting in the jungle was that del Castillo wanted to tell Guzman's story in a movie.
The attorney general said that her office is not interested in the movie-making plans, but in del Castillo's tequila business and whether she received drug money.
"We have an investigation into the tequila angle; we are not investigating her plans to make a movie," Gomez told El Universal. "Our investigation is focused."
Del Castillo is not required to travel to Mexico to give a statement; she has the option of giving it at her nearest Mexican Consulate, Gomez said.