The tractor-trailer truck was found on Monday evening next to railroad tracks in a remote area on the city's southern outskirts, Xinhua news agency reported citing local media as saying.
San Antonio is located 250 km from the US-Mexico border.
Addressing reporters, San Antonio Fire Chief Charles Hood said that emergency responders initially arrived at the scene at about 6 p.m. after responding to reports of a dead body, the BBC reported.
"We're not supposed to open up a truck and see stacks of bodies in there. None of us come to work imagining that," he was quoted as saying.
The fire chief added that the vehicle had no working air conditioning and there was no drinking water inside.
Also addressing the media, the city's Police Chief William McManus said federal agents were going to investigate the incident, adding that three people were currently being held in custody.
San Antonio Mayor Ron Nirenberg said the development was "nothing short of a horrific, human tragedy", adding: "They had families...and were likely trying to find a better life."