Police in Zachary, a Baton Rouge suburb, said they don't know how the woman died.
"I couldn't tell if it was blunt force trauma. It was definitely homicidal," Zachary Police Capt. David McDavid said.
He said the body awaits an autopsy in Terrebonne Parish, 80 miles away.
McDavid declined to identify the man because his wife's family hasn't been notified.
"About 12:20 p.m., he walked in, said he wanted to speak to an officer and blurted out that he just killed his wife," McDavid said.
After he was advised of his rights and searched for weapons, McDavid said, the man told investigators "he had killed his wife, and she was in his vehicle in the back parking lot."
Investigators verified that the woman was dead and had roped off the car as a crime scene when the man said that she had died about 5:30 or 6 a.m., outside a Burger King in Houma.
Terrebonne Parish investigators drove to Zachary - usually about a 2½-hour trip - to interview the man. He was booked as a fugitive from Terrebonne Parish, McDavid said.
