Without even considering whether or not I would support the purpose for which it was written, I can't imagine it passing constitutional muster - on its face it violates both the Fourteen Amendment's "equal protection" clause and Title VII of the Civil Right Act of 1964.
If what they want to accomplish is "ensure that corporate boards are not made up entirely of men", then the law should have been written to say that in a way that is not gender-specific - instead of definition "female", it should have defined "minority gender", and required minimum numbers of the minority gender on boards of given sizes.
There's also the small consideration that as far as I can tell, a corporation that has only one shareholder of record can have a board with only one member. This bill appears to literally make it illegal for anyone who does not self-identify as a woman to form and operate such a corporation. Existing corporations in this class would be forced by law to add an additional board member if and only if the owner is not female. That's absurd.