"I deeply regret any confusion or discomfort that my recent words have caused," added Hernandez, who won two Premier League titles during his five-year spell at United.
He said he was "listening, reflecting and committed to expressing myself with better clarity and sensitivity" and he would "take this opportunity to understand, grow and continue working to be a better version of myself".
The original comments, which were made last weekend, were met with a backlash in Mexico.
President Claudia Sheinbaum, the country's first female president, said: "Chicharito is a very good soccer [player] but when it comes to his opinion on women... he still has a lot to learn."
In a joint statement, the FMF and Mexico's top men's and women's leagues said the Gender and Diversity Commission has started an investigation "that seeks to prevent and punish this behaviour", and it will "take more severe measures in the event of a repeat offence".
Chivas said the comments were "contrary to the principles and values" of the club and they had taken "appropriate action" against Hernandez, though they did not specify what that was.
Hernandez, Mexico's all-time leading scorer, joined Manchester United from Chivas in 2010.
Spells with Real Madrid and Bayer Leverkusen followed, before he returned to the Premier League in 2017 with West Ham for a three-season stint.
Hernandez left them for Sevilla, before spending four seasons with MLS side Los Angeles Galaxy.
He returned to first club Chivas in 2023, signing a two-year deal.