In the clip, which Saudi Arabia's Labour Ministry described as "offensive," the burqa-clad woman is seen eating and waving to the camera before she appears to feed the man, who is outside the frame.
The video of the two, who are both hotel workers, sparked outrage on Saudi social media, especially over the part in which the man appears to be fed by the woman.
Besides arresting the man, the Labour Ministry reportedly also summoned the owner of the hotel "for failing to adhere to government regulations that stipulate a gender-segregated workplace."
Saudi Arabia has for decades imposed strict social rules, including bans on alcohol, music and mixing of unrelated men and women.
Much of that is now changing under Crown Prince Mohammed bin Salman who curbed the powers of the religious police in 2016 as part of ambitious social and economic reforms.
Unrelated men and women are increasingly allowed to enter family sections of restaurants together, and public events have generally done away with such divisions.
Many Saudis, however, are concerned that changes are happening too fast and fear they could provoke a backlash from religious conservatives once seen as dominant.