The van, carrying 17 people, was headed east on I-40 at about 2 a.m. The driver did not notice traffic ahead was stopped and the van "under-rode the back end of a tractor-trailer," Santa Fe County Undersheriff Benjie Montano said.
"There didn't appear to be any signs of braking" by the van, he said.
Thirteen people in the van died - 11 at the scene - while four others were hospitalized, Montano said.
"The seats had been gutted and they had been just sitting on the floor," Montano said.
All the occupants of the van were believed to be Mexican nationals, and authorities were investigating whether they had entered the United States legally, he said.
The crash occurred between Edgewood and Moriarty, roughly 35 miles east of Albuquerque. Although the road was icy, visibility was clear, Montano said.
A storm had left 3 inches of snow at Moriarty and 2 inches of snow at Edgewood - where wind-blown snow drifted to depths of 16 inches.
The tractor-trailer rig had been stopped behind other traffic that had been backed up because of another crash, Montano said.
One person died en route and one died shortly after arrival at University Hospital, where two others - a man and a woman - were in satisfactory condition and another man was in critical condition, spokeswoman Cindy Foster said. Another man was in critical condition at Presbyterian Hospital.
Eastbound traffic on I-40 was diverted around the crash for several hours before reopening. The storm blew west-to-east through the state beginning Friday and was lingering over New Mexico's north and east side Saturday morning.
Three years ago, on the same highway, four mariachi musicians from Mexico were killed when their overloaded van was struck from behind by a tractor-trailer rig on Dec. 11 between Santa Rosa and Clines Corners. The van carried 12 members of a mariachi band from the Monterrey, Mexico, area.