It happened just after 7 a.m. on Plank Road west of Wayside Drive Wednesday morning.
Investigators said an Army vehicle taking part in a convoy rolled over.
All three soldiers were assigned to the 4th Military Information Support Group (Airborne). Their identities were not released.
Military Police said they were looking for the driver of a white, or light colored, Chevrolet Impala with dark window tint and halogen lights for questioning in the incident.
Anyone with information is asked to contact the Fort Bragg Military Police Station at (910) 396-0391/(910) 396-0392 or the Fort Bragg CID Office at (910) 396-8777.