The announcement, made after the weekly Cabinet session last evening, offered no details about Princess Reema bint Bandar's role.
Physical education is not on the curriculum for Saudi girls in public schools and ultraconservative clerics shun women's exercise as "immodest."
Women's teams are not part of the kingdom's federation that oversees sports and stadiums are male-only.
Even so, the kingdom is sending four female athletes to the Olympic games in Rio, marking the second time that Saudi women will participate in the Olympics.
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A separate government portal shows the agency is responsible for issuing licenses to establish new sports centers and handles youth registration in sports. The sports authority could not be immediately reached for comment.
In a decree in May, King Salman ordered the General Presidency for Youth Welfare to be renamed the General Authority for Sports. The former body had sponsored cultural and sports activities for youth.
In April last year, the king sacked the most senior woman in government, Nora al-Fayez, from her post as deputy education minister for girls.
Princess Reema, whose father Prince Bandar bin Sultan served as Saudi ambassador to Washington for more than two decades until 2005, is a graduate of George Washington University with a degree specialising in museum studies, Islamic art and architecture.
In the kingdom, she is widely known for having served as chief executive officer of the upscale Harvey Nichols department store in the capital, Riyadh, which was among the first retailers to hire women as sales clerks.
Also this week, Saudi newspapers reported that a court in the Eastern Province has approved the appointment of the country's first female commercial arbitrator. It marks the first time a woman has been appointed to such a post.