Saudi Arabia is planning this year to loosen restrictions on women’s ability to travel without a male guardian’s permission, officials and people familiar with the matter said, in a step away from the system of male domination deeply rooted in Saudi society.

The plan would end guardianship laws pertaining to travel for men and women over 18 years old, allowing them to leave the country without the consent of a designated male family member, the people said. Currently, women of any age and men under 21 need a guardian’s permission...