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It was the brainchild of Ferrell and his longtime collaborator Adam McKay, director and co-writer of Anchorman: The Legend of Ron Burgundy and Talladega Nights: The Ballad of Ricky Bobby.
It co-stars McKay's 2-year-old daughter, whose real name is Pearl, but does not curse like that when off camera, McKay tells PEOPLE.
"Fortunately she is in this great stage now where she repeats anything you say to her and then forgets it right away, which is key," says McKay, who has two daughters by his wife of 11 years, actress Shira Piven (Jeremy's sister).
Adds McKay, "She has not said the B-word since we shot the thing."
The video was shot on a lark a little over a month ago in Ferrell's guesthouse during a break in the third birthday party for Ferrell's son Magnus.
"We invited a friend with a camera over and shot it in about 45 minutes," says McKay, who set up the website, Funnyordie.com, as a platform for his and his friends short form comedy films. "We shot several shorts but we liked this one the best. I am not sure that it is the funniest – it is just that you can't beat Will being cursed out by a 2-year old."