UNHCR's office in Canada did not immediately respond to MEE's request for comment on Friday.
Rahaf Mohammed Alqunun, 18, was stopped last Saturday at a Bangkok airport by immigration police who denied her entry and seized her passport.
Under Saudi Arabia's "male guardianship system", a Saudi woman is required to obtain a male relative's approval to apply for a passport, travel outside the country, study overseas on a government scholarship, get married, leave prison, or even exit a shelter for abuse victims.
But Australian Home Affairs Minister Peter Dutton told reporters on Wednesday and that Alqunun wouldn't get any "special treatment" and was no different from any other similar case.
The foreign minister there, Marise Payne, met with senior Thai officials in Bangkok on Thursday.
"Canada has been unequivocal that we will always stand up for human rights and women's rights around the world", he said. He called on Twitter to shut down those accounts.
A Twitter user known as Nourah, whom Qunun has referred to as a friend, tweeted that Qunun "received death threats and for this reason she closed her Twitter account".
"Canada is very concerned by and watching closely the situation of Ms Rahaf al-Qunun", spokesman Stefano Maron told MEE.
She raised Australia's concerns with Thai officials about Hakeem al-Araibi, a 25-year-old former member of Bahrain's national soccer team who was granted refugee status in Australia in 2017 after fleeing his homeland, where he said he was persecuted and tortured.
Ms al-Qunun has also claimed her family would kill her if she were sent home to Saudi Arabia, where she has renounced Islam and "rebelled" against her father.
Canada has granted asylum to an 18-year-old Saudi teenager who was feeling abuse from her family in Kuwait. But after being detained by Thai authorities, she refused to board a flight back to Kuwait.
But late Friday Thailand's immigration police chief said she was bound for Canada. She made it to an airport in the Philippines, but despite the scene she made with her desperate pleas for safety and freedom, Dina was last seen screaming and being dragged onto a Saudi Arabia Airlines flight from Manila to Riyadh.
If she goes there, her case could add another interesting element to what has been an escalating back-and-forth between Canada and the Saudi government, a spat that has severely strained relations between the two countries.
World football governing body FIFA says Mr.al-Araibi should be freed and allowed to return to Australia where he plays for Melbourne football club Pascoe Vale in the second tier of the Australian League.
"The Thai government is most certainly aware of the importance of this matter to Australia", she said.
Her possession of an Australian tourist visa and very public expression of interest in going to Australia put pressure on Canberra to take the lead.
Qunun's case has drawn worldwide attention to the strict rules many Saudi women face and comes at a time when the Gulf country is under increased scrutiny following the gruesome murder of Saudi journalist Jamal Khashoggi.