Another 60 people were unconscious, the Pakistani newspaper Dawn reported.
Witnesses said the driver pulled into a truck stop, looked into the container and fled in a car. Storeowners and truck drivers called police.
Police Deputy Inspector General Wazir Khan Nasar told Dawn the driver was believed to have made several attempts to cross the border into Iran but was turned back. The immigrants apparently began their trip in Spin Boldak, Afghanistan.
Baluchistan, a sparsely inhabited province bordering Iran and Afghanistan, has become a popular route for smuggling would-be immigrants to western Europe.
Those in the container were all Afghan nationals, many of them members of the Uzbek, Tajik and Hazar groups.