"Harvey would be proud to know that his legacy continues to teach us to believe in ourselves and our dreams," said Leno, D-San Francisco, in a prepared statement.
The bill would designate May 22, Milk's birthday, as Harvey Milk Day in California, and encourage schools to teach students about Milk's life and contributions.
The bill passed the Assembly by a 45-23 vote, according to Leno's office. It will now move to the state Senate for consideration.
Leno said the bill is intended to give gay, lesbian, bi-sexual and transgender, as well as heterosexual students, "a positive representative of who LGBT people are that inspires pride and self-esteem rather than fear and shame."
Milk was elected to the San Francisco Board of Supervisors in 1977, becoming the first openly gay official of any large U.S. city, and the third openly gay official in the country.
Milk and former San Francisco Mayor George Moscone were assassinated on Nov. 27, 1978 by former Supervisor Dan White.