In a joint statement issued on Wednesday by FMF alongside Mexico's premier men's and women's leagues — Liga MX and Liga MX Femenil — officials indicated that the 37-year-old striker's comments violated their gender and diversity policies and amounted to a form of media violence.
The football organizations added that Hernandez made comments on social media that "encourage sexist stereotypes".
FMF imposed a monetary penalty and issued a warning, stating that more severe repercussions could follow if Hernandez repeats such actions.
"I sincerely regret any confusion or discomfort my recent remarks may have caused; it was never my aim to restrict, hurt, or divide...," Hernandez shared on social media on Thursday.
"I am open to listening, reflecting, and dedicated to expressing myself with more clarity and sensitivity, particularly on such delicate matters. I believe that change starts within oneself.
"I will seize this opportunity to learn, grow, and continue striving to be a better version of myself, rooted in honesty, love for my family, my values, and love for all of you..."

Hernandez shared videos over the weekend where he urged women to "allow themselves to be guided by a man" and criticized women for "eradicating masculinity".
Hernandez, Mexico's all-time leading scorer, also claimed that society has become "hypersensitive" and questioned feminist perspectives on domestic roles.
The comments were broadly condemned as sexist and disconnected from modern society, eliciting backlash from fans and public figures, including Mexican President Claudia Sheinbaum.
Hernandez returned to his childhood club Guadalajara last year after playing for several top European teams, including Manchester United, Real Madrid and West Ham United.