Abu Taleb was defeated by Mobina Nematzadeh of Iran in the bronze medal play-off in the -49kg division of the taekwondo competition played out inside Paris' spectacular Grand Palais.
The 27-year-old had won her last 16 clash against Israel's Abishag Semberg before losing her quarter-final against Panipak Wongpattanakit of Thailand, the gold medallist from the Tokyo Olympics.
She secured a place in the bronze medal play-off by seeing off Morocco's Oumaima El Bouchti 2-0 but the high-ranked Nematzadeh proved too strong.
Abu Taleb had qualified for the Games by bagging gold at the 2020 Arab Taekwondo Championship and bronze medals at the Asian and world championships in 2022.
Earlier this year she upgraded to gold at the Asian Taekwondo Championships.
Saudi women had previously fared badly at Olympics.
In 2012 in London, judoka Wojdan Shaherkani became the first Saudi woman to compete at the Olympics but her historic debut lasted just 82 seconds, as she was beaten in the first round.
US-born Sarah Attar, another invitee, finished a distant last in her 800m heat on the track.
Attar was one of four Saudi women to compete as wildcards at the 2016 Olympics, and they were followed by two more at Tokyo 2020.
