The arrests come just hours after a video capturing the incident went viral on social media, sparking controversy among users.
The incident had also led Saudi Arabia's Prince of Assir governorate, Faisal bin Khaled, to order an immediate investigation into the matter.
In a statement he made on Thursday's episode of Rotana Khalijiya's Ya Hala program, head of Assir governorate's media and communications office, Saad Al Thabet, confirmed news of the arrests.
He also added that the man who's at the center of the controversy told investigators the woman seen in the video is his sister.
Though they have yet to verify his claims, an investigation into the case is ongoing and the duo will soon be referred to public prosecution.
News of the arrests is now making the rounds online
A few people were all for the decision
"Even if he was one of her male guardians, this is still inexcusable. There's something called respect for public sentiment, social norms, traditions, and values."
And thanked authorities for taking action
Others were having none of that though
"I don't know why you don't accept people who are just living normal lives. Where's the problem in what they did? It's their personal freedom."
"Their mistake is that they danced in a society that blows everything out of proportion"
People expressed their anger over the arrests
"To be honest, you blew this entire incident out of proportion. The action taken against these people is shocking and bizarre. They didn't commit a crime that warrants their arrest."
Others raised this important point
"A teacher beating up his student, that's acceptable. A drug addict father abusing his child, beating his head against a car, that's fine, you'll say he's just disciplining him. A husband hitting his wife and dragging her across a street, that's normal, you'll say she deserves it. A woman covered from head to toe, dancing with a man who's standing two meters away from her in a street, that's an unacceptable, scandalous act."