Police were investigating whether the vehicle was involved in human smuggling. They were searching for one person who was in the van but ran off after the wreck on Interstate 70 about 30 miles from the Colorado line.
Authorities said four passengers were thrown from the 1999 Toyota Sienna as it rolled down the middle of I-70 at about 4:30 a.m., authorities said. It was unclear whether they were the four who died.
Investigators don't know what caused the crash, but they believe no other vehicles were involved, Utah Highway Patrol Sgt. Todd Royce said.
Photos released by authorities show a smashed windshield and right door, and at least one missing wheel.
Police were still investigating and did not yet know how old the passengers were, where they were from or who was driving the minivan. The survivors apparently do not speak English, Royce said.
Emergency crews brought the hurt passengers to St. Mary's Hospital and Regional Medical Center in Grand Junction, Colorado. Their injuries ranged from serious to critical, Royce said.
The crash shut down the interstate, backing up eastbound traffic for 5 miles, Utah Department of Transportation spokesman John Gleason said.
Gleason said traffic was flowing normally at about 10:15 a.m., approximately an hour after officials reopened one eastbound lane.