Rahaf Mohammed al-Qunun refused to board a flight from Bangkok to Kuwait on Monday and barricaded herself into her airport hotel room.
She said she feared her family would kill her for renouncing Islam.
She is now staying at a Thai government shelter while the UN refugee agency assesses her case.
Her father and brother have arrived but she is refusing to see them.
Renunciation of Islam, known as apostasy, is punishable by death in Saudi Arabia.
Thai immigration officials had initially said she should return to Kuwait.