There were a total of nine patients. Six were listed in critical condition and two were flown to a Phoenix hospital, said Phoenix Fire Department Deputy Chief Frank Salomon.
Salomon told The Associated Press the accident happened when the riders got too close to the big rig.
"It appears the garbage truck collided with the group of motorcyclists. There was fire involved. It's a horrific scene," Salomon said.
The crash occurred in the area of 27th Avenue and the Carefree Highway around noon.
Jarrod Cook, a worker at the nearby Ketzal Mexican Grill, said he saw several motorcycles wedged underneath the garbage truck, which caught fire.
"The first thing we saw was a big puff of smoke when the truck lit on fire," he said.
Cook said he walked over and witnessed a chaotic scene with some of the injured lying on the ground.
Dozens of police and rescue personnel responded to the crash off Interstate 17.
Witnesses told CBS News Affiliate KPHO-TV in Phoenix that people inside a nearby Walgreens rushed out with fire extinguishers to help put out the fire.
Phoenix Fire Department spokesman Jonathan Jacobs told KNXV-TV in Phoenix that witnesses reported that several motorcycle riders were stopped at a light when they were struck from behind by a sanitation truck and dragged 50 to 75 yards.
The three riders killed were trapped under the truck and the injured included four males and two females, Jacobs said.
The 50-year-old driver of the truck was not injured and is being questioned by police.
The Carefree Highway was expected to be closed for several hours as police investigate the crash and determine exactly what happened.