Judicial Watch, a conservative activist group, is suing California for a new law that requires publicly traded companies based there to include women on their boards.

California should not use government funds to carry out a “brazenly unconstitutional” gender quota, according to the group, which filed a lawsuit Aug. 6 in Los Angeles County Superior Court on behalf of three individuals.

Former Gov. Jerry Brown acknowledged “serious legal concerns” when he signed the law last year, the first of its kind in the U.S. It calls on California-based companies to have at least one woman on their boards by the...