"The three small children had to be hospitalised... because of the extremely bad state of their health. Doctors said they were treated for severe dehydration," police said in a statement about the incident on Friday morning.
"If the journey had continued the situation could probably have become critical," a spokesman from police in Upper Austria state told AFP.
The vehicle, pulled over by police after a chase, contained 26 "illegal foreigners" from Syria, Bangladesh and Afghanistan who said they wanted to go to Germany, police said.
The incident happened near Braunau am Inn in western Austria close to the border with Germany. The Romanian driver, who had refused to pull over for a routine check, was arrested.
On Thursday an abandoned truck containing the bodies of 71 dead migrants including four children was found on a motorway in eastern Austria near the Hungarian border, provoking international revulsion.
Children were the first to die
Austrian daily Oesterreich calculated Saturday that the 71 were crammed into 15 square metres (160 square feet) and would have asphyxiated in 63 minutes once they were shut inside the refrigerated truck with no air, the children suffocating first.
Autopsies were still being carried out but police think that the migrants, likely from Syria, suffocated from lack of air and had been dead for up to two days before the refrigerated truck was noticed by motorway maintenance workers.
Austria borders Hungary, which has seen more than 140,000 migrants enter from Serbia this year, most of whom then seek to travel onwards to western European countries like Germany and Sweden, via Austria.
'Horrified and heartbroken'
The tragic discovery highlighted the dangers faced by people fleeing conflict and hardship in the Middle East and Africa even once they reach Europe, with many putting their fate in the hands of profit-hungry people smugglers.
Saying he was "horrified and heartbroken" by the gruesome discovery and by a new Mediterranean shipwreck off Libya claiming at least 111 lives, UN Secretary General Ban Ki-moon said Friday it was high time for concerted action to tackle the crisis.
Libyan rescue workers said Saturday that "dozens" of people were still missing after a boat carrying around 400 would-be migrants sank Thursday off the country's western shores. A total of 198 people have been rescued.
The United Nations estimates 300,000 people have fled conflict and hardship in the Middle East and Africa for a better life in Europe this year. Some 2,500 have died in the attempt, mostly in the Mediterranean.
"My little sister, someone climbed on her back and pushed her down. When I saw her for the last time, she was underwater with him on top of her," Pakistani Shefaz Hamza, 17, a survivor who also lost his mother in the latest tragedy, told AFP in Libya.
Meanwhile, a Hungarian court on Saturday remanded in custody until at least September 29 four suspects in the deaths of 71 migrants found in an abandoned truck in Austria.
"The period of preliminary detention of the four suspects has been extended to September 29," the head judge of the court in Kecskemet, Ferenc Bicskei, told a press conference.
"If charges are not filed by the investigating prosecutors by that date, but the judge considers that there is reasonable cause to extend this period, then it can be extended beyond that date," added Szabolcs Sarkozy, a spokesman for the court.
Police believe the three Bulgarians and one Afghan -- aged 29, 30, 50 and 28 respectively -- include the owner of the truck found on an Austrian motorway on Thursday and its drivers.
They suspect they are low-ranking members of one of the numerous and often unscrupulous human trafficking gangs that prey on many of the tens of thousands migrants coming to Europe.
Prosecutors said they want them kept in detention due to the "exceptional nature of the crime, the subsequent deaths of the smuggled persons and the perpetration of the criminal act of people-smuggling in a businesslike manner."
Migrants keep coming
An AFP reporter on the Greece-Macedonia border said migrants were continuing Saturday to cross in groups of 50.
One of them, Ali Younes, a 65-year-old from Baghdad, sold his home in Baghdad to pay a smuggler to reach Turkey through Syria. He risked his life in an inflatable boat to get to the Greek island of Samos from Turkey.
"I lived through everything: the Iran-Iraq war, the invasion of Kuwait, the sanctions period, the US occupation, the sectarian war, and now Daesh," he told AFP, referring to the Islamic State extremist group that has seized chunks of Iraq and Syria.
Meanwhile in Germany, which expects to absorb 800,000 asylum seekers this year, between 2,000 and 4,000 people demonstrated in the eastern city of Dresden on Saturday in solidarity with refugees.
"Say it loud, say it clear, refugees are welcome here," they chanted. A poll by broadcaster ZDF showed 60 percent of Germans agreed with Merkel that Europe's biggest economy can accommodate the new arrivals.