The code would allow surrogate pregnancies, broader rights for grandparents in regard to grandchildren, protection of the elderly and measures against gender violence.
President Miguel Díaz-Canel, who has promoted the law acknowledged questions about the measure as he voted on Sunday.
The measure had been approved by Cuba’s Parliament, the National Assembly, after years of debate about such reforms.
But there is a strong strain of social conservatism in Cuba and several religious leaders have expressed concern or opposition to the law., worrying it could weaken nuclear families.
That has meant a greater opening not only the once-dominant Roman Catholic Church, but also to Afro-Cuban religions, protestants and Muslims.