The 30-year-old, a gold-medallist in the four-man bob in 2010, was admitted to hospital with acute appendicitis in Gangneung on Monday night, a week before the two-man competition begins.
"We are hoping Justin will recover quickly enough to compete in the two-man race," USA Bobsled and Skeleton chief Darrin Steele said in a news release.
"The timing is unfortunate and we are heartbroken for Justin, but he's shown us over the years that he's capable of overcoming adversity and coming out on top."
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Olsen moved up to the front of the sled after helping the American four-man team to 12th place in Sochi four years ago and was one of three pilots selected in the United States team.
"We know he's going to do what he can within his power to be at the starting line on race day," Steele added.
"There's no question he's mentally ready, but we are looking at our options in case he physically can't compete."
Doctors usually recommend rest for one to three weeks after a laparoscopic appendectomy before a patient resumes normal activity.
(Reporting by Nick Mulvenney, editing by Sudipto Ganguly)
