She had been due to present a special award to Luther Vandross and open the music awards with Justin Timberlake, who exposed her right boob when he ripped open her jacket during the American football showpiece's half-time bash last Sunday.
Justin, 23, said he expected her to be wearing a bustier beneath.
The lawsuit claims that Janet's exposure and other "sexually explicit conduct" caused viewers to "suffer outrage, anger, embarrassment and serious injury".
The papers state, "Employees of corporate defendants knew or should have known Ms. Jackson and Mr. Timberlake were including the act of Mr. Timberlake ripping off part of Ms Jackson's costume to expose one of her breasts.
"All of the defendants knew that the Super Bowl would be watched by millions of children.
"Families have an expectation that they can trust companies and individuals not to expose families to sexually explicit conduct."
However,Janet, 37, has repeatedly apologised for the stunt.