A series of videos, initially posted to the Snapchat account of "Model Khulood", show a young woman in a high-waisted miniskirt walking through a fort in Ushaiqer, outside the capital Riyadh, playing with sand in the dunes and turning towards the camera for a close-up, her long hair uncovered.
The videos have since been uploaded to YouTube and tweeted by different users.
The local government of Riyadh has issued a memo saying authorities were taking the "necessary measures" to find the woman, who it accused of "walking around... in indecent clothing".
The Commission of the Promotion of Virtue and the Prevention of Vice -- Saudi Arabia's "morality police" -- on Sunday also confirmed it was investigating the case in coordination with "relevant authorities" via Twitter.
The snaps have sparked heated debate, with social media users in the region and beyond weighing in on questions of gender and rights in the kingdom, where women are required to wear long black abaya robes and cover their hair in public.
"If it were Trump's daughter, we would have braced ourselves for the flood of compliments and love poems," read one tweet.
"Problem solved," tweeted Shahd bint Fahd alongside a picture of the model with Ivanka Trump's face superimposed over the original.
Others expressed outrage and derided those speaking out in support of the model.
"These are the demands of the liberal ignorant community: a naked woman, a co-ed movie theatre, and music and dance. That's progress to them! Not health care and not education," read one tweet.