West sustained the concussion after being hit in the head during Saturday's practice.
The Chiefs didn't offer a timetable for the return of the 27-year-old West, who had 18 carries for 72 yards and two touchdowns in 13 games last season. He also had 27 receptions for 150 yards and two scores.
The Kansas City Star reported that the Chiefs are without their top three running backs due to various injuries. Kareem Hunt is nursing an ailing hamstring and Spencer Ware is dealing with a knee injury.
Offseason acquisition Damien Williams took the bulk of the first-team snaps in 11-on-11 work this past weekend. Williams signed a one-year, $1.5 million contract in the offseason after spending the last four years with the Miami Dolphins.