Cole was in "extremely good condition" but was taken to University Medical Center as a precaution, Las Vegas police Capt. Vincent Cannito said. He was treated and released to his father's care early Sunday, hospital spokesman Rick Plummer said.
Even before the good news, Cole's grandfather, Clemens Tinnemeyer, had been arrested. Police said they believe the kidnapping at gunpoint may have been a message to Tinnemeyer, 51, who authorities say may have stolen millions from drug dealers involved in trafficking methamphetamine.
Tinnemeyer was scheduled to appear before a federal magistrate Monday in Riverside, Calif. He was arrested there Friday and was being held in nearby San Bernardino on a material witness warrant issued by a federal court in Nevada.
Las Vegas police didn't know whether Tinnemeyer had a lawyer. Police have declined to elaborate on what role he played in the drug operation or whether the kidnappers had been seeking a ransom.
Messages left at a number believed to be for the Tinnemeyer home were not returned. A black pickup truck sat in the driveway Sunday, but no one came to the door.
FBI spokesman David Staretz said authorities continued the search Sunday for another "person of interest," a Mexican citizen identified as Jesus Gastelum.
Gastelum, who is in his mid-30s, is believed to be in Las Vegas or Southern California, police said. Another "person of interest" in police custody Saturday was not identified.
Cole's father, Robert Puffinburger, was a picture of relief at a news conference, as he smiled, cried and thanked police and neighbors for helping to bring Cole home.
"I'm just so glad he's safe," his father said.
A bus driver for the disabled discovered Cole walking alone on a residential street, said Jacob Snow, a general manager for the Regional Transportation Commission of Southern Nevada. The driver pulled over to see if he was OK.
"Cole approached the bus and asked the driver, 'Can you take me home?'" Snow said.
The bus driver, who did not want to be identified, took Cole onto the bus and contacted police, Snow said. The child told the driver and riders that he had been dropped off just a few minutes before.