The victim, Harry Whittington, 78, was said to be in good condition in a Corpus Christi hospital after being shot while hunting quail with the vice-president.
Cheney sprayed Whittington, a lawyer from Austin, Texas, with shotgun pellets while hunting quail at about 5.30pm local time on Saturday at the Armstrong Ranch in Kenedy County.
Cheney is a frequent visitor to the ranch, the local newspaper, Corpus Christi Caller-Times, reported.
Katharine Armstrong, owner of the ranch, said Whittington had been taken to Christus Spohn Hospital Memorial by ambulance.
Lea Anne McBride, a spokeswoman for the vice-president, was reported as saying: "The vice-president has spoken with Mrs Whittington and is visiting with Mr Whittington today."
CNN television, citing a witness, said that Whittington had never lost consciousness.
"Nobody wants this to happen, but it does"
Lea Anne McBride,
spokeswoman for Dick Cheney
The vice-president would return to Washington later on Sunday, NBC News reported.
Armstrong said Cheney, 65, had turned to shoot quail that had just been flushed out, accidentally peppering one side of Whittington's body. Armstrong said Cheney had been unaware Whittington had approached him from behind.
"Nobody wants this to happen, but it does," she told the paper. Cheney's secret service agents tended to the injured man before paramedics arrived, Armstrong said.
Officials with the Kenedy County Sheriff's Office had helped investigate the incident, the paper said.