The gunman, whose name wasn't immediately released, was flown by medical helicopter about 75 miles to University Medical Center in Las Vegas. His condition wasn't immediately made public.
Empey, a Mesquite police officer for more than 15 years, was taken to Mesa View Regional Hospital in Mesquite. He was treated and later released, Smith said.
Empey was the first Mesquite police officer wounded on the job, said Capt. Chris Jones, the Las Vegas police administrator heading the investigation.
The Mesquite Police Department has 27 sworn officers. It has never had an officer shot and killed on duty, Jones said.
Empey was in a marked patrol car and a detective was in an unmarked police vehicle when they stopped the gunman and a woman in a 1996 Geo Metro with Utah license plates on Sandhill Boulevard, Smith said.
The scene was near a fast-food restaurant just south of the Interstate 15 exit at Pioneer Boulevard.
The officers were investigating an earlier unspecified incident in Mesquite, the police spokesman said. The detective's name wasn't immediately made public.
Officials didn't say whether Empey, the detective or both fired shots. Smith said police recovered the revolver allegedly used by the gunman.
The 48-year-old woman in the vehicle wasn't injured, and her name wasn't released. Smith said she was from Richfield, Utah.
The woman was detained at the Mesquite city jail for police questioning. Smith described her as cooperative and said she wasn't immediately charged with a crime.
Las Vegas police detectives were handling the shooting investigation, and prosecutors from the Clark County district attorney's office went to the scene.
Mesquite, on the Nevada-Arizona state line, is a former Mormon settlement that has grown to about 20,000 residents, including many retirees. It has several casinos and golf courses in the Virgin River valley.