BBC reports they were reportedly convicted for promoting corruption, prostitution and propaganda.
The video showed them dancing by Tehran's Azadi (Freedom) Tower.
Authorities are handing heavy sentences to people seen to be involved in protests after the death of a woman who was detained by morality police.
The couple did not link their dance to the ongoing protests in Iran.
A source has confirmed to BBC Monitoring that the couple's arrest came after they posted the video to their Instagram accounts, which have a combined following of nearly two million.
