Erath County Sheriff Tommy Bryant said Kyle, 38, and a second man were found dead at Rough Creek Lodge's shooting range west of Glen Rose, according to the Fort Worth Star-Telegram and Stephenville Empire-Tribune. Glen Rose is about 50 miles southwest of Fort Worth.
Bryant did not immediately return phone calls to The Associated Press seeking comment late Saturday and early Sunday. A woman who answered the phone at the lodge where the shooting occurred declined comment and referred calls to the sheriff's office.
Investigators did not immediately release the name of the second victim, according to the newspapers.
Witnesses told sheriff's investigators that a gunman opened fire on the men around 3:30 p.m. Saturday, then fled in a pickup truck belonging to one of the victims, according to the Star-Telegram. The newspapers said a 25-year-old man was later taken into custody in Lancaster, southeast of Dallas, and that charges were expected.
Lancaster police did not immediately return calls for comment.
The motive for the shooting was unclear.
Kyle wrote the best-selling book, "American Sniper: The Autobiography of the Most Lethal Sniper in U.S. Military History," detailing his 150-plus kills of insurgents from 1999 to 2009.
Kyle was sued by former Minnesota Gov. Jesse Ventura over a portion of the book that claims Kyle punched Ventura in a 2006 bar fight over unpatriotic remarks. Ventura says the punch never happened and that the claim by Kyle defamed him.
Kyle had asked that Ventura's claims of invasion of privacy and "unjust enrichment" be dismissed, saying there was no legal basis for them. But a federal judge said the lawsuit should proceed. Both sides were told to be ready for trial by Aug. 1.