In the ruling, a lower court in the northern Japanese city of Urawa ordered the Nagano Olympic Organizing Committee (NAOC) to pay the ski jumping fan 3,560 yen ($28.88).
The man sued NAOC because a bus used to transport spectators to the ski jumping venue arrived after the event had finished because of heavy traffic.
The award was made even though NAOC had refunded the man's event ticket and bus fare.
"NAOC has a duty to pay compensation to the plaintiff after causing the man mental anguish because of the missed event," Judge Fukutaro Fuji said in his ruling.
NAOC had refused to pay for a train ticket the man bought to take him from his hometown to Nagano. The amount awarded by the court was about equal to the cost of that ticket.
"We made compensation within the extent of our responsibility and believe we responded with all sincerity," NAOC said in its submission to the court.
Speaking after the verdict, a NAOC spokesman said they were disappointed by the decision and would appeal against it.
"We are worried that this decision may persuade other people on the same bus to sue us," the spokesman told Reuters.
"This could affect not only other Olympics but also other international sports events anywhere in the world in the future."
Transport problems and bad weather plagued the early part of the February 7-22 Winter Games.
Hundreds of people either never made it or were late in getting to the ski jumping venue on February 11, a national holiday. The event was the most popular for Japanese.
A Japan Olympic Committee spokeswoman said the court case was a lesson for the Olympic movement.
"The Olympic side didn't delay the bus on purpose. It just happened. We see this incident as a lesson, and we just have to try not to repeat such an incident," she said. ($1=123.28 Yen).
Reuters
