The afternoon pileup occurred on Interstate 10 north of Picacho Peak, KNXV-TV, Phoenix, reported.
Arizona Department of Public Safety officials said several commercial trucks were involved in the multiple collisions, including some tipped over on their sides, the TV station said.
Police identified the first of the three people killed as George Lee Smith, 77, of Mead, Wash., The Arizona Republic reported. Smith's wife was injured and was being treated, the newspaper said.
Traffic on I-10 was closed in both directions because of the crashes. KNXV-TV said motorists were being encouraged to avoid the area for the next several hours.
Visibility as low as 10 feet had been reported in the area as dust was sent flying by high winds.