The stench from the container suggested some of the immigrants may have been dead for days, Rasool Bakhsh, a police spokesman, said.
The victims were ethnic Tajiks, Uzbeks and Hazaras from Afghanistan's Paktika province. They were thought to have been travelling to Iran through Pakistan.
Their final destination was said to have been Turkey, where they hoped to find work.
The group had been trapped inside for 24 hours and many people died from lack of oxygen, police said.
Wazir Khan Nasir, a senior police official in Quetta, said: "We have been able to talk to some of the people who were trapped in the container.
"When the condition of people inside the container deteriorated, the driver fled."
The driver was later arrested and taken for questioning by the police.
Dozens of the survivors were unconscious and taken to hospital for treatment.
Officials said the death toll is expected to rise.