According to the Saudi daily Okaz, the woman strongly objected to the policeman's interference and repeatedly punched him so hard that he ended up in the hospital with bruises to his face and body.
The couple, believed to be in their 20s, were strolling through an amusement park in the city of Al-Mubarraz when the policeman asked them to confirm their relationship to one another.
No statement on the incident has so far been made by the religious police – formally titled the Commission for the Promotion of Virtue and Prevention of Vice – or by the regular police, the Arab site and The Jerusalem Post reported.
If the unidentified woman is charged she could face a long prison term, as well as body lashes.
"To see resistance from a woman means a lot," Wajiha Al-Huwaidar, a Saudi women's rights activist, told The Media Line News Agency, The Post reported.
"People are fed up with these religious police, and now they have to pay the price for the humiliation they put people through for years and years," she was quoted as saying. "This is just the beginning and there will be more resistance."
"The media and the Internet have given people a lot of power and the freedom to express their anger," she added. Whatever the religious police do ends up all over the Internet, she said, which gives them "a horrible reputation and gives people power to react."
Under Saudi law, women are not allowed to drive, be seen in public without a male guardian and socialize with unrelated men.
A decision to open the country's first co-educational university last year was strongly criticized by a senior Saudi cleric, who was then fired by King Abdullah, The Post reported.