The company was in the process of accounting for all its employees at the site at 34511 Lyndon B. Johnson Freeway.
Employees on site were again seeking shelter as there were more tornados in the area around 3 p.m., Schneider National spokeswoman Janet Bonkowski said.
The operating center is described as one of the company's larger facilities in the area.
The building did not sustain major damage in the storm, but the loss of equipment in the yard was described as "massive."
CNN showed video from WFAA in Dallas of an apparent tornado in Dallas County, Texas, ripping though an area packed with trucks and trailers. Several of the trailers — including many in the distinctive orange of Schneider National — in the video were tossed high into the air before falling back to the lot.
"Drivers go there for maintenance, for fueling and its where their driver mangers are located," Bonkowski said about the operating center. "It's one of the hubs."
The National Weather Service reported at least two separate "large and extremely dangerous" tornadoes south of Dallas and Fort Worth.
Dallas Police spokeswoman Sherri Jeffrey said an apparent twister touched down and caused damage within the city's southern limits.
Officials had no immediate information about injuries.
The weather service said "considerable damage" also was reported near Cleburne, south of Fort Worth, and Lancaster, south of Dallas.