Rahaf Mohammed al-Qunun, 18, had been trying to reach Australia via Bangkok, but was initially told to return to Kuwait, where her family were waiting.
She refused to fly back and barricaded herself into her airport hotel room, attracting international attention.
She said she had renounced Islam, which is punishable by death in Saudi Arabia.
The UN's refugee agency has said it considers her to be a legitimate refugee.
Thai immigration officials had initially said she should return to Kuwait, where her family were waiting.
She then started a social media campaign, live-tweeting her case and attracting international attention.
Refugee status is normally granted by governments, but the UNHCR can grant it where states are "unable or unwilling to do so", according to its website.
Thai immigration officials told Reuters that Canada had "granted her asylum", however Canadian officials told the BBC they currently have "nothing to confirm" on the issue.