The women, in their 20s, said they had arrived in the former Soviet republic of Georgia and needed help from the international community to find a new country to call home.
"We are in danger. We need your support to deliver our voice. We want protection. We want a country ... (that) welcomes us and protects our rights. Please help us," the pair wrote on a shared Twitter account named GeorgiaSisters.
The case is the latest to draw attention to Saudi Arabia's strict social rules, which force women to obtain the permission of a male "guardian" if they want to work, marry or travel.
Rights groups say the system can trap women and girls as prisoners of abusive families, and the sisters are not the first Saudi women to seek urgent refuge outside their homeland.
The sisters, who identified themselves as Maha al-Subaie, 28, and Wafa al-Subaie, 25, posting photos of their passports online, said they were seeking protection from the United Nations refugee agency (UNHCR).
They initially said they had become stranded in Georgia after the Saudi government suspended their passports and that members of their family had come looking for them, but later retracted this version of events.
"We are confused," they wrote.
"We are terrified as (we've) never been before. Been crying all the time not knowing what's next. We do not feel safe," they said in a tweet that was later cancelled.
Georgia's interior ministry said the sisters had not asked for asylum or any help.
Nino Kajaia, a UNHRC spokeswoman in Georgia said the agency could not discuss individual cases due to confidentiality.
The Saudi embassy in Tbilisi did not immediately reply to a request for comment.
Earlier this year, a Saudi teen who had holed up in a Thai airport hotel to escape her family won asylum in Canada.
In 2017, a Saudi woman who had sought asylum in Australia, saying she feared violence from relatives, was stopped on a layover in the Philippines and returned to Riyadh.
Separately on Wednesday, a Saudi court postponed a hearing in the trial of several women rights activists who had campaigned for the right to drive and an end to the guardianship system. Shortly after their campaign, the kingdom got rid of the driving ban in a move that won positive headlines worldwide.
Yet some of the women who had fought for that very right said they were subjected to torture in detention, be it electric shocks, flogging or sexual assault - something authorities deny.
Suad Abu-Dayyeh, Middle-East consultant for women's rights group Equality Now, said Saudi women were treated as minors and second-class citizens because of the guardianship system.
"This creates an oppressive situation, both inside the family environment and within the country as a whole, so it is understandable that many women and girls want to escape," she told the Thomson Reuters Foundation.
"The U.N. and international community need to place greater pressure on the Saudi Arabian government to give women and girls the liberty to freely exercise their civil rights in their own country, and without persecution."
The lifting of the driving ban, which for years drew international condemnation, was welcomed by Western allies as proof of a new progressive trend in Saudi Arabia.But it has been accompanied by a crackdown on dissent, and many Saudis fear the reforms could provoke a backlash from religious conservatives once seen as dominant.