Brian Heidik, 38, who is charged with battery and cruelty to animals, said in a bond hearing that he believed the dog was a coyote that had been harassing his pets, WSB-TV reported on its Web site.
But Douglas County Chief Deputy Stan Copeland said it was a puppy.
"At about 3 a.m., his wife called to report that he was outside and that he had shot a puppy that was on his property with an arrow and planned to shoot another one," Copeland said, adding that Heidik's wife and 5-year-old son were at home at the time.
When sheriff's deputies arrived, Heidik fled in his car but was quickly caught and taken back to the home where the incident occurred.
Authorities took custody of the wounded puppy and the second puppy and were trying to determine to whom they belonged.
Heidik did not immediately respond to a message from The Associated Press left on an answering machine at one of two phones listed in his name in Douglasville, Ga., about 21 miles west of Atlanta. There was no answer Wednesday afternoon at the second number.
Heidik, a former used-car salesman and part-time actor, won the $1 million prize as the sole survivor of "Survivor: Thailand," the fifth edition of the CBS adventure game show. It was broadcast from September to December 2002.
Heidik's TV acting credits include appearances on "Baywatch Nights," "Doogie Howser, M.D." and the soap opera "Days of Our Lives." His film credits under the name David Roth include "Chick Street Fighter," and "Virgins of Sherwood Forest," according to IMDB.com, the Internet movie database.