The film, created by Gravity Road, shows five men doing a choreographed dance to Dance of the Sugar Plum Fairy by Tchaikovsky in front of a surprised audience in a community hall.
The video was directed by Ben Turner through Fulwell 73 and created by Pete Conolly, Gravity Road's new creative director.
Meera Folkes, the digital marketing manager at Sainsbury’s, said that the retailer wanted to do something "unexpected" to launch the jumpers.
She said: "Judging by the response, there’s now going to be even more dad dancing across British homes this Christmas." The video was shared more than 18,000 times in the first 48 hours of launch.
As Facebook told Campaign in October, the social network is making a concerted effort to challenge YouTube’s video dominance.
Maureen McDonagh, a client partner at Facebook, said: "The Tu at Sainsbury’s campaign is a brilliant piece of content, and brilliant content gets talked about.
"Coupled with the fact that Christmas is traditionally the most active time of the year on social media, it shows how Facebook is coming into its own as a channel for entertainment and discovery."