Cruise's attorney, Bert Fields, said to falsely claim the actor deserted his daughter post his divorce from Katie Holmes is a "vicious lie", the Daily Mail reported.
"Tom is a caring father who dearly loves Suri. She's a vital part of his life and always will be. To say it in lurid headlines with a tearful picture of Suri is reprehensible."
The lawsuit against the publishers of Life & Style magazine was filed in a Los Angeles federal court and Fields said that if the actor wins, he will donate the money to a charity.
Cruise and Holmes divorced earlier this year after a six year of marriage.
Fields said that the actor doesn't like to file lawsuits but felt it was appropriate because the tabloids were trying to make money about his relationship with his daughter, Fields said.