Alanoud AlFayez, 57, a Jordanian national who has lived in London since her divorce from the Saudi monarch in 2003, said her children needed to be "saved".
Her comments come ahead of Obama's visit to the kingdom on Friday, during which US lawmakers have urged him to address rights violations in Saudi Arabia.
"Since 13 years, my daughters Sahar, Maha, Hala and Jawaher are being held captive," AlFayez told AFP. "They need to be saved and released immediately."
AlFayez, who married the Saudi king when she was only 15, said her daughters had recently had their twice-monthly trips to buy food, water and medicine for themselves and their pets stopped.
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Her eldest daughter Sahar, 42, has complained about her situation on the social media website Twitter.
"We have no passports or ID, we are under house arrest, with little food left for ourselves and pets," she told AFP in an email, without saying how she had access to the Internet.
She accused the royal family and members of the household of "unlawfully detaining" them and of "physically and psychologically abusing us for years."
Diplomats in Saudi Arabia said the princesses were being kept in Jeddah but were able to move around in the city accompanied by bodyguards.
Roland Dumas, the lawyer for Alanoud AlFayez and a former French foreign minister, said they had applied to the UN High Commission for Human Rights in Geneva in October regarding the case but had received no response.
Dozens members of the US Congress have urged Obama to bring up the prickly subject of rights in Saudi Arabia, including efforts by women activists to challenge the country's ban on female drivers, despite recent tensions over Washington's efforts to reach a nuclear deal with Iran and its reluctance to engage more forcefully in Syria.