The agent was taken to a hospital after the 4:30 a.m. shooting near the community of Arivaca and several people were detained, a Border Patrol Statement said, providing no information on the agent's injuries or the circumstances of the shooting.
Jim Chilton, a fifth-generation Arizona cattleman who runs a 50,000-acre (about 20,230-hectare) ranch outside Arivaca, told The Associated Press in an interview that the Border Patrol sent him an email saying the agent was alone when he was wounded on the ranch and was struck in the leg and the hand.
Several bullets also struck the agent's protective vest, which probably saved his life, Chilton said.
"Without it, he probably would not be with us today," said the rancher, a well-known Arizona backer of President Donald Trump's efforts to secure the U.S.-Mexico border.
The Border Patrol official who the rancher said wrote the email, Lisa A. Reed, did not immediately respond to an email seeking confirmation of the details Chilton provided. Border Patrol spokesman Chris Sullivan declined to comment.
Arivaca is southwest of Tucson and about 10 miles (16 kilometres) from the border.
About 200 trails meander over Chilton's ranch and he said the area where the shooting happened is along the most travelled trail. One 14- mile (22-kilometre) side of his ranch is separated from Mexico by a four-strand wire fence.
"We have drug runners coming through our ranch and this has become a very dangerous situation," Chilton said.