The Swede, considered a strong medal contender coming into the event, was leading when a gust caught his skis as he flew over the final obstacle.
He crashed on landing, causing Russia's Egor Korotkov and Jouni Pellinen of Finland to hit the deck behind him and allowing Swiss Armin Niederer the victory.
A photo-finish revealed Korotkov's hand had crossed the line first, allowing him second place and a spot in the semis, while the Swede was eliminated.
"I had a good run, I was fourth out of the gate and was passing very easily, I had everything under control," Oehling Norberg told reporters.
"The wind caught my skis, I started rotating and there was nothing I could do."
Oehling Norberg, who won the Olympic test event in Sochi in 2013, is leading the World Cup standings.
He reached the knockout stages here as fastest man in the seeding runs, won his race in the last 32 and had looked well set for a medal.
"It's ski cross, it's always that tight. It's just really disappointing that I crashed," the 23-year-old said.
Asked how he would change things next time, Oehling Norberg deadpanned: "Keep my skis aligned."
- Sports & Recreation
- Egor Korotkov
- Jouni Pellinen