Winston Watts, 46, revealed the runners were missing after the team's baggage was lost in transit, the Russian sports news agency R-Sport reported.
"We've got a backup plan. A lot of people want to help us, and we can take part with backup runners," Watts said after his team arrived in Krasnaya Polyana, Russia.
The Jamaican bobsled team, comprised largely of former track athletes, first competed at the 1988 Winter Olympics and was popularized by the 1993 film "Cool Runnings." Its presence in Sochi was underwritten by an Internet fundraiser, R-Sport said.