Women were first allowed to take part in the 1900 Paris Olympics Games, and since 1991 all new sports wanting to be included must include a women’s event.
The first royal woman I found to have joined the Olympics was Queen Sofia of Spain, then still a Princess of Greece and Denmark. She took part in the 1960 Olympics as a reserve in sailing. Her brother Constantine won Gold with the Dragon.
Her daughter Infanta Cristina (previously also Duchess of Palma de Mallorca) was also an Olympian. She participated in the 1988 Seoul Olympics Sailing, just like her brother Felipe. She was also the standard-bearer for Spain.
For the United Kingdom Anne, Princess Royal participated as a member of the equestrian team in the 1976 Montréal Olympic Games. She ended as 26th in the individual competition, and as a team, they ended up as 9th.
Her daughter, Zara Tindall, followed in her footsteps and joined the 2012 Olympic team. She won a silver medal with the Great Britain Eventing Team and was presented the medal by her mother. She also carried the Olympic Flame.
Princess Haya of Jordan was on Jordan’s Equestrian team for the 2000 Sydney Olympic Games for show jumping. She was also Jordan’s flag bearer.
Charlene, Princess of Monaco, participated in the 2000 Olympic Games for swimming for South Africa and finished in 5th-place in the 400 medley relay team.
Princess Nathalie of Sayn-Wittgenstein-Berleburg was a reserve for the 2000 Sydney Olympic Games. She was a member of Denmark’s dressage team for the 2008 Beijing Olympics, where she won a bronze medal. She also competed at the 2012 London Olympic Games.