Victor Brabble, a spokesman for U.S. Customs and Border Protection, told the Los Angeles Times the agent, whose name had not been disclosed, had left the hospital.
Authorities had yet to make any arrests in the shooting, which took place early Tuesday near Naco, about 100 miles south of Tucson and 5 miles north of the Mexican border, the Times said. Law enforcement officers on horseback, driving all-terrain vehicles and in helicopters combed the area where the shooting took place looking for clues, the newspaper said.
The FBI and the Cochise County Sheriff's Office are heading up the investigation with assistance from other agencies.
The body of slain agent Nicholas Ivie was transferred Wednesday from a Tucson funeral home to Sierra Vista, KPHO-TV, Phoenix, reported.
Ivie and two other agents were checking a border sensor that had been set off when they came under fire. The third agent, who also hasn't been identified, as not injured.
Ivie, 30, a Provo, Utah, native, leaves behind a wife and two young children.
"We are extremely proud of Nick and for his service both in his community and our country," his parents and brothers said in a statement. "He loved what he did and he gave it his all, including his life. Our thoughts and prayers are with his wonderful wife and his two beautiful girls."
President Barack Obama called Ivie's family to express his condolences, the White House said.
Ivie is the third border patrol agent killed this year and the 14th since 2008, CNN said.