Rahaf Mohammed al-Qunun, 18, who fled from her family and barricaded herself inside a Bangkok airport hotel to prevent Thai authorities expelling her, was allowed to leave the airport after talks with the United Nations refugee agency late on Monday.
Rahaf al-Qunun has said she fears her family will kill her if she was forced to return home.
Alqunun's father - a senior Saudi official - and her brother, who she says often physically abused her, are now in Thailand.
Ms Hanson-Young said Australia should offer "sanctuary" to Ms Qunan so she can live in a country that "respects women and girls".
The spokesperson said the government had "serious concerns on this matter and the need for Ms Al-Qunun's claim to be assessed expeditiously".
At 3.30pm on Monday, Thailand's immigration chief Surachate Hakparn held a press conference at the airport for dozens of Thai and global media representatives gathered in the transit area.
"Yesterday, they [social media supporters] made the difference in Rahaf's life", she said. "Please help me." Instead, she was reportedly "dragged onto a plane from Manila to Riyadh with her mouth taped shut and her arms and legs bound".
"Because this is a high profile case and because she has a lot of support from the worldwide community, I think it is very possible that this could end very quickly", said Phil Robertson, deputy Asia director at Human Rights Watch.
Alharbi mentioned the case of Dina Ali Lasloom, a 24-year-old Saudi woman who in April 2017 was returned to Saudi Arabia from the Philippines against her will and whose fate is unclear.
Although Canadian officials said diplomats routinely raise human rights issues with their Saudi counterparts, the Saudi government reacted strongly to the public appeal and retaliated by freezing new trade, recalling its students from Canada and cancelling flights between the two countries.
We now know she is safe, in the care of the UN Human Rights Council in Bangkok awaiting a decision on her request for asylum in Australia or Canada.
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Alqunun said she planned to seek asylum in Australia, fearing she would be killed if repatriated by Thai immigration officials who stopped her at the airport. "I want asylum", she added in a video uploaded to twitter.
She later tweeted she feels safe under United Nations protection and has gotten back her passport, which had been taken from her earlier.
The statement, which described al-Qunun's case as a "family affair", said the kingdom did not demand her deportation to Saudi Arabia.
A spokesman for the UN High Commissioner for Refugees said the agency would look into Alqunun's claims but it was "too early to tell" if she will be granted refugee status.
"Shouting out for help of humanity", another read.
"I wish you had taken her phone, it would have been better than (taking) her passport", the official said.
Thai immigration chief Surachet Hakparn, speaking to journalists outside the Saudi Embassy after meeting with Saudi officials in Bangkok on Tuesday, said officials are concerned about Qunun's safety and well-being.
The Saudi embassy in Bangkok declined to comment on Ms Qunun's case when contacted by Reuters on Monday and could not be reached on Tuesday.
"We are very grateful that the Thai authorities did not send back Ms. Al-qunun against her will and are extending protection for her", UNHCR Thailand country representative Giuseppe de Vicentiis was quoted as saying in a statement released on Tuesday morning. "She didn't get that [social media] support and that's why she's in Saudi Arabia now - she's disappeared", Alharbi said.
She had asserted her independence and renounced Islam but had been forced to pray, wear a hijab and was beaten by her brother.
Saudi Arabia's human rights record has been under heavy scrutiny since the murder of journalist Jamal Khashoggi past year.