The decision followed a complaint by Fatima al-Baghli, a Kuwaiti woman who petitioned the court for the right to obtain a passport without her husband's consent.
She said her husband had refused to give her and their three children their passports and other personal identification documents in an effort to prevent them from leaving the country, The Associated Press news agency reported.
Thousands of petitions
Al-Baghli was one of thousands of women who have been petitioning courts for the right, the AP said.
The ruling is the latest gain for women in Kuwait since they were granted the right to vote and compete in elections in 2005.
Earlier this year, four women were elected to the Kuwaiti parliament for the first time.
Aseel al-Awadhi, one of the four MPs, welcomed Tuesday's ruling as a "victory for constitutional principles".
She said the ruling "puts an end to this injustice against Kuwaiti women", but said she will continue to work to change other legislation that violates the constitution.
Activists say they are still fighting for equal access to government housing and the right for women to pass their citizenship to their children.