The desperate men were found inside the lorry on the A41 outside a Tesco in Bicester, Oxon, around 6.30pm on Tuesday night.
Thames Valley Police said they were called by one of the men who believed they had been in the back of the lorry for 48 hours.
After being removed they were checked by paramedics and then detained by immigration officials.
The driver of the lorry was arrested.
Charles Brown, from Kirtlington, was on his way home from picking his two children up from karate when he saw the lorry being pulled over and dashed to get provisions.
Mr Brown, 45, said: "I've seen this happen before there so I recognised what was going on.
"I nipped into a shop to buy a load of bottles of water. If you're stuck in a lorry for two days the first thing you want is probably a drink of water.
"My children were very upset by it - we're all human. The police were really really good thankfully. It was very calm."
Police said: "Around 6.30pm last night we were called by a man who said he and a number of other men were in the back of a lorry.
"Officers located the lorry on the A41, Wendlebury, Bicester. 16 men were checked over by the South Central Ambulance Service, no one required hospital treatment.
"This investigation has now been handed over to Immigration Enforcement."