The agent was trying to arrest the man just after 7:15 p.m. on the U.S.-Mexico border east of Lukeville, Ariz., Customs and Border Protection (CBP) said in a statement.
"As the agent attempted to arrest the subject, a physical altercation ensued, and the agent discharged his firearm, striking the subject," CBP said.
The agency said the injured man was flown to a Phoenix hospital with non-life-threatening injuries. The border agent was not harmed.
The FBI and the CBP Use of Force Incident Team are investigating the shooting.