It was signed by 10 liberal, independent and Shia lawmakers, but no Sunni Islamist or tribal MPs put their signatures to the motion submitted on Wednesday, which is to be debated by the 50-seat house in two weeks.
The signatories want the court to rule on the constitutionality of article one of the law, which limits voting rights and candidacy to male citizens above 21 years of age.
They said the law violates Kuwait's constitution which stipulates gender equality.
The motion requires a simple majority vote in its favour.
The move came two days after parliament approved a list of priority issues to be debated in the current term, which comes to an end in June. It did not include a bill approved by the government last May to grant women their rights.
Kuwaiti women have called for
full political rights since 1963
In November 1999, a bill granting Kuwaiti women their full political rights, put forward by Amir Shaikh Jabir al-Ahmad al-Sabah, was rejected by parliament under pressure from Islamist MPs and tribal leaders.
After presenting his government's legislative programme to parliament in July 2003, liberal-leaning Prime Minister Shaikh Sabah al-Ahmad al-Sabah promised to renew efforts to amend the election law in women's favour.
Kuwaiti parliamentary elections are scheduled for July 2007.
Out of a total Kuwaiti population of 956,000, only 140,000 men are eligible voters.
Kuwaiti women have been pressing for their political rights since 1963 when the oil-rich emirate held its first elections to the National Assembly which enjoys limited powers but can legislate.
Women activists have repeatedly taken the issue to the constitutional court, which has rejected the claims on technical grounds.