The former head of Amazon Mexico is wanted for questioning after his wife was apparently killed in Mexico City.
Abril Pérez Sagaón was shot dead in a car on Monday in front of two of her teenage children.
Juan Carlos García has not commented publicly.
The couple were in the middle of a divorce battle and García had been freed on bail after a prior allegation of violence against her.
Pérez said he had beat her with a baseball bat when she was asleep in January.
García was held in pre-trial detention for 10 months, but the judge released him at the start of November, downgrading the charge to domestic violence.
The judge who released García questioned the intent of the alleged crime, saying that if he had wanted to kill her, he could have done so as she was sleeping at the time.
She had a restraining order against her husband and was trying to get custody of their three children.
She was killed after a motorcyclist ambushed her vehicle while she was on her way to the airport. However, no charges have yet been issued.