Friday's shooting outside a sheriff's office substation in Surprise, Arizona, was the second time a county deputy has come under fire this month, Arpaio said.
The sheriff said a gunman parked his car outside the substation and "fired several times" at a deputy, who escaped injury after positioning himself by a bullet-resistant door.
Neither the suspect's name nor the charges against him were released.
The motive for the shooting is unclear. Arpaio said it was the second "ambush" against one of his deputies in two weeks.
"There's a war on cops," the tough-talking sheriff told CNN affiliate KPHO-TV
in Phoenix. "They better start thinking about that all the way from Washington on down."
On May 7, Maricopa County sheriff's Deputy Bryan Wisda suffered non-threatening injuries after a gunman in a passing car opened fire on him, according to Deputy Joaquin Enriquez.
Wisda made a DUI enforcement traffic stop in Tempe when someone in a silver Cadillac sprayed him and his patrol car with gunfire, Enriquez said. The suspect then fled.
The deputy was released from a hospital two days later. The motive in that shooting remains unknown.
The outspoken sheriff has drawn criticism for his treatment of prisoners and opposition to undocumented immigrants.
Known as "Sheriff Joe," Arpaio calls himself America's toughest sheriff. His headline-grabbing actions have earned him diehard supporters and fiery opponents.
Last week, a federal judge ruled Arpaio was in civil contempt
in connection with a racial-profiling case. Three of Arpaio's subordinates also violated court orders, the judge found.
In July, the U.S. Justice Department settled a lawsuit against Arpaio and his office that alleged discrimination and the unlawful detention of Hispanics.