U.S. authorities say Jeremiah Cross, 34, Crystal Cross, 32, and seven-month-old Grayson Cross were among the victims in the crash on Interstate 95, which also took the lives of two Pennsylvania residents.
Maj. Brian Lepack, acting commanding officer of 2 Service Battalion at Garrison Petawawa, northwest of Ottawa, says Cross was a private who joined the Canadian Armed Forces almost three years ago and was training to be a vehicle technician.
Media outlets in South Carolina say the crash happened Saturday night on the northbound lanes of the heavily travelled interstate in Florence County, which is about 100 kilometres northwest of Myrtle Beach.
The collision, which is still under investigation, involved five vehicles, including two tractor trailers.
Two of the cars in the crash caught fire. Traffic on the northbound lanes of the interstate was blocked for about 12 hours.
Lepack said Cross was well liked by his peers and the shock of his death has been felt by all who knew him.
"We all share in the loss of this fine young man and his family. Our focus now is on supporting Jeremiah's family, and all members of our unit," Lepack said in a statement Monday afternoon.
"The death of a soldier at any time is difficult but this accident, which claimed the life of this young soldier, his wife and young child, is a tragedy which affects us all whether we are military or civilian," Lepack said.
The U.S. victims have been identified as Jacqueline McCann, 51, and Barry Himes, 52, both of Johnstown, Pa.
— With files from The Associated Press