The court, whose decisions are final, said the previous requirement was in violation of guarantees of freedom and gender equality in the constitution.
The decision came about when a woman complained her husband had prevented her from leaving the country.
The country's first female MPs were elected in May 2009.
The article abolished by the court dated back to Kuwait's 1962 passport law which required a husband's signature on a woman's passport application.
Aseel al-Awadhi, one of the new MPs, welcomed the passport law ruling as a "victory for constitutional principles that puts an end to this injustice against Kuwaiti women".
It is the latest gain for women in the oil-rich Gulf state which has made a number of strides towards gender equity in recent years.
The presence of female MPs followed the granting of equal political rights in 2005.
Women voted for the first time in 2006 - albeit in segregated polling booths - in a by-election where they made up 60% of eligible voters.
Kuwaiti women enjoy more freedoms than in neighbouring Saudi Arabia, where there is strict gender segregation and women are not allowed to drive cars.
Women activists welcomed the passport ruling but say they still need equal access to government housing and the right to pass citizenship to their children.