The 30-year-old Scot, who has been suffering from a virus, was almost overtaken during the four-kilometre test by the Australian Bradley McGee in the last of the nine heats as he trailed in with the 11th fastest time of 4min 34.297sec.
Earlier, Obree, the world champion, saw his world record of 4:20.894 - set three years ago in Norway - shattered by Andrea Collinelli. The Italian's time of 4:19.699 was almost five seconds inside the Olympic record of 4:24.496 registered by Britain's Chris Boardman four years ago at the Barcelona Games.
Not satisfied with his performance, the Italian then reduced the world record for the second time, cutting it to 4:19.153.
"Obviously I'm very disappointed," the Scot said. "But my form this year just hasn't been up to it and that's what happened here. I made a reasonable start, but then went over 16 seconds and that's where it all started to go wrong.
"I had the chest infection in May and June and there were signs of it here when they did the blood tests, but it's a bit late in the day for that."
Obree, who has had a sore throat and a respiratory infection in the build- up to his event, had been hoping to emulate Boardman's 1992 Barcelona Games success in this discipline.
It was clear from the start that he was struggling in the searing heat and stifling humidity as McGee opened up a lead of 1.663sec after the first lap. The Australian increased that to 2.262 by the second lap, 2.766 by the third and 3.369 by the fourth. By the fifth lap, he had nearly reached Obree's slipstream.
McGee was then content to coast through to the quarter-finals with the fifth fastest time of 4:27.954.
Ireland's Phil Collins also bowed out after managing only the 16th fastest time of 4:41.207 when he rode in the opening heat against the South African David George.
There was further disappointment for Britain in the 1km time trial when Shaun Wallace finished 16th - 3.744 seconds behind winner Florian Rousseau, of France, who lowered the Olympic record to 1:02.712.Reuse content