The actress and activist was honored for her work on behalf of women Monday night
“I don’t preach to her every day,” she told PEOPLE on the red carpet prior to receiving an award from Equality Now at the Make Equality Reality event in Beverly Hills on Monday. “She’s aware that her mommy fights for the rights of women, that there are many places in the world where they are not entitled to the rights.”
Hayek, 48, also shared that her daughter is a “big fan” of Malala Yousafzai – and that the Pakistani activist for female education is making an important impact on her impressionable child.
“She understands who she is and what she does,” she said. “Because of this, it makes her appreciate her own opportunities for education. She knows everything I do for Chime for Change (the women’s charity she cofounded with Beyoncé) and how important it is in my life. That’s all I can do. Just try to live an example of the things I believe in.”
While accepting the award, Hayek also explained why equality for women is so critical and her passion for the charity.
“It is your choice to decide what is going to be your contribution to your lifetime in the world,” she said. “If it’s going to be about women, we will provide the tools so you can know what’s going on. The next step is to create a coalition of warriors who want to create war against violence and against hate.”
Despite her passionate support for women, Hayek told PEOPLE that she does not consider herself to be a feminist.
“I am not a feminist,” she said. “If men were going through the things women are going through today, I would be fighting for them with just as much passion. I believe in equality.”
• Reporting by MATTHEW COLE WEISS