It's believed a tyre blow out may be to blame for the accident, in which the van skidded and hit the centre guide rail, tipping over.
Police said that 32 people had been accounted for but that they believe there are likely to have been more refugees crammed in the back of the van and that some may have run off after the accident, and could also be injured. A spokesman from the fire service said that there were also children in the back of the van.
Police spokesman Johann Baumschlager said that refugees were seen running down the A1 after the crash and that it was lucky motorists were able to stop in time, preventing further accidents and possibly deaths.
Emergency teams, including an air ambulance, were called to the scene of the crash and the A1 was temporarily closed in the direction of Salzburg.
The injured refugees were taken to hospitals in St. Pölten and Amstetten, and others who were in shock were cared for by the Red Cross.
The man who was driving the van ran off before police arrived and they are now searching for him with sniffer dogs and a helicopter with a thermal imaging camera.
On Tuesday another van attempting to smuggle refugees through Austria crashed on the S1 road near Vienna, with 45 people in the back. Several were injured.
Last week a suspicious van which turned out to be smuggling 17 refugees was pursued by a police car in Burgenland and drove into a ditch. Three people were injured.