The 15-year-old model recalled in the new issue of Teen Vogue how she found out Crawford was a celebrity during her eighth birthday party.
"I think it was only on my eighth birthday, at Disneyland, that I started to understand what was going on," she told the magazine. "I wanted to take pictures with the princesses, and everyone wanted to take pictures with her!"
Gerber is the daughter of Crawford, one of the top supermodels of the 1980s and 1990s, and Rande Gerber, a model-turned-businessman. Her brother, 18-year-old Presley Gerber, has also followed in their parents' footsteps as a model.
"As my brother and I get older and busier, I really cherish the time we spend together," Gerber said. "Every summer we go to our house in Canada; it's our tradition. It's on the lake, and we go for four or five weeks. There's no Wi-Fi, so I stay off social media."
Gerber signed her first major contract with IMG Models at age 13 in 2015, and has since landed campaigns with Alexander Wang and Marc Jacobs. She shared her parents' advice in the interview for keeping true to herself amid success.
"My parents have always taught me to be myself and to follow my instincts," the teenager said. "They also say that you should never let what other people do affect what you want to do. It changes everything when you accept who you are and you don't try to change yourself."
Gerber previously said at the Daily Front Row Fashion Media Awards that Crawford taught her more than modeling. She praised her mom for encouraging her "to be kind, punctual ... and to stand up for [herself]."