Investigators have not found any history of domestic or mental health problems at the home, and still have no leads as to a possible motive in the killing, said Clayton police Lt. Jon Gerrell.
Amber Violette told police Friday evening she had found her daughter, Katlin, with her head severed from her body, police said.
An "edged weapon" believe to have been used in the killing was found in the house, though Gerrell declined to give more details.
"This is devastating for the whole community as a whole, and it's the most horrific thing I've seen in 13 years of police work," said Sgt. S.P. Lapsley. "That a father could do this to his child, I just can't believe it."
John Patrick Violette's vehicle was found at Raleigh-Durham International Airport, and investigators learned he had taken a flight to Washington. Deputy U.S. marshals arrested the 37-year-old after police tracked his credit card to the hotel, Lapsley said.
Police said Violette, 37, would be held in Washington pending an extradition on a murder charge expected to be filed in Clayton, about 15 miles southeast of Raleigh. The U.S. Marshals Service said an extradition hearing is expected to be held Tuesday.
The mother is not a suspect in the investigation, and Lapsley said police don't expect to make any more arrests.
Police said John Violette quit his job at a home improvement store on Thursday, the News & Observer of Raleigh reported.
Lori McCreary, who lives across the street from the Violette home in Clayton, a suburb about 15 miles southeast of Raleigh, described the family as "very private, but normal."
"They went to church every Sunday. They just seemed like a very happy, normal couple," McCreary said. "This is just so very, very shocking -- and devastating."