The two girls and one boy aged 5 and 6 had been in a dire state when police stopped the van after a high-speed chase close to the town of St. Peter am Hart on the border with Germany, a spokesman for Austrian police said. They are now recovering in hospital.
"The emergency doctor told us they would not have made it much longer - two, maybe three hours," said David Furtner, police spokesman for Upper Austria province.
"The driver did not give a damn about the people in the back. We would not transport animals under these conditions on our roads in Austria."
The incident follows the discovery of the corpses of 71 refugees in an abandoned truck on an Austrian highway on Thursday, victims of an unfolding tragedy as refugees and migrants fleeing conflict and poverty in Africa, Asia and the Middle East flock to Europe in unprecedented numbers this year.