Arizona Department of Public Safety officials identified one of those killed as George Lee Smith, 77, of Mead, Washington.
They said Smith's wife was injured, but her condition wasn't immediately disclosed.
DPS officials said 19 vehicles - 10 commercial vehicles, seven passenger cars, one tanker and one recreational vehicle - were involved in chain-reaction collisions south of Casa Grande shortly after noon.
Television footage showed that several cars and tractor-trailers smashed into each other near Picacho Peak in south-central Arizona, with at least one passenger car pinned between two 18-wheelers and others wedged under big rigs.
Medical helicopters airlifted several of the injured to hospitals in Tucson and Phoenix, and DPS officials said at least one person was in critical condition.
The names and hometowns of the other two killed weren't immediately available, authorities said.
The Picacho Peak area is prone to dust storms that develop suddenly and can quickly reduce visibility to zero for drivers.
The National Weather Service had issued a blowing dust advisory shortly before the crashes, with wind gusts of up to 30 mph reported in the area.
DPS spokesman Bart Graves said Tuesday's crash was one of the worst chain-reaction accidents in that area in the past seven years.
Parts of the westbound lanes of I-10 at the crash scene were closed for more than five hours.