It will only apply to Sunnis since Shi’ite MPs opposed the Jaffari section following complaints from religious leaders.
Al Wefaq bloc – an all-Shi’ite line-up – yesterday withdrew from the debate.
It had threatened to veto the original bill containing a section for Shi’ites if it was not withdrawn.
The Sunni MPs at the session voted for the law without any major amendments to the government draft, which was referred to parliament last month.
The law deals with marriage, divorce, alimony and custody cases.
Shi’ite MPs had earlier claimed only senior clerics should have the power to come up with such a law, with six religious leaders.
Domestic disputes are resolved in Sharia courts, with separate systems for both sects.
Sharia judges base verdicts on their interpretation of Islam, but a Family Law would standardise procedures.
Women’s rights activists have long campaigned for the law, saying the existing system fosters discrimination against women.
The government welcomed the law and said it represents Bahrain’s new civilised aspect. Justice and Islamic Affairs Shaikh Khalid bin Ali Al Khalifa said it would help reduce domestic problems and divorces. The Shura Council will study the law.