The girl was flying unaccompanied by an adult.
Savannah, Ga., lawyer Mark Tate, who represents the family, says Delta is responsible for some of the trauma the girl suffered because the airline is required by law to take extraordinary measures to ensure passengers' safety.
"No one is saying here that Delta is a dishonorable company or a poorly run airline," Tate said. "Mistakes can be made, and a mistake that shouldn't have been made caused a little girl to really be traumatized."
Tate says the girl - who is not named in the lawsuit - reported the assault to her mother when she got off the plane Jan. 6.
But authorities have filed no criminal charges and have not identified a suspect.
The alleged molester switched seats with the girl "so she could sit beside the window," and it's possible he switched seats with other passengers, too, Tate said.
The case likely will require identification by the girl rather than trying to match passenger names with seat assignments, he said.
The girl was returning from a visit to her father, a United States Marine scheduled to be deployed to Iraq.
On The Early Show Monday, the girl's mother, whose identity was concealed and who wasn't facing the camera, told co-anchor Hannah Storm, "(My daughter) expressed to me that she had been moved to first class, and I wanted to know exactly why, because I know that she was seated in the coach area. And she expressed to me that it was a guy on the plane with her, and he, he started to touch himself inappropriately while rubbing her face and her legs.
"Well, he started to rub her legs, and she asked him, 'What are you doing?' You know. And he stopped, and he removed his hand from her leg, and he went to the restroom, and he came back and he started it again, and once he started it again, I guess she was frightened, and she didn't say anything. I have no answers for the reason she didn't say anything, but ..."
The mother added that her daughter alerted a flight attendant to what was happening: "When she sat down in that seat, the flight attendant came around and served her the snacks, and that's when she expressed, while the guy was at the bathroom, she asked, could she be removed? And (the flight attendant) said, 'No, you'll be fine. I'll just check on you.' "
The girl's father, identified only by the name Eric when interviewed from San Diego, told Storm he was very upset and angry, adding, "A kid's flying on a plane, they should be with other kids or up front with stewardess supervision, but that wasn't the case. She ... shouldn't have been sitting by a grown man."
The parents say the girl had flown alone before, with no problems.
The mother reported the incident to police in Huntsville, Ala., and Atlanta and to the FBI, Tate said. Police in Atlanta and Huntsville are not investigating the charges, spokesmen for the departments said.
Spokesmen for the FBI offices in Atlanta and Birmingham - which oversee the Huntsville office - said their offices are not investigating the incident, either. The Birmingham office has no record of the mother's call, spokesman Paul Daymond said.
He also said that if any other FBI office were investigating the incident, his office would be aware, because they would be asked to do the interviews with the family.
Delta has special rules for keeping a close watch on children flying alone, an airline spokeswoman said. The airline is investigating the incident, said Delta spokeswoman Betsy Talton.
She declined further comment because of the pending litigation.
The suit was filed in Fulton County (Georgia) State Court.
The girl's mother is a 31-year-old property manager from Huntsville.