The Scots runner was going well until she appeared to be clipped by a runner behind her, causing her to fall back.
McColgan finished in a time of 15:09.68 but her tenth-place finish wasn't enough to carry her through to the finals.
Gudaf Tsegay of Ethiopia finished first in 14:55.74, with Kenya’s Hellen Obiri coming in second. Nadia Battocletti of Italy finished third with America’s Elise Cranny and Norway’s Karoline Bjerkeli Grøvdal taking the remaining qualifying slots.
McColgan’s Team GB team-mate Amy-Eloise Markovc finished in ninth place in 15:03.22.
Speaking to Eurosport after the heat McColgan said: “I'm so tall and my legs are so long that it's not even that I clip people's feet, I clip people's hands.
"But that is racing, I know that's the way it is. Obviously I'm absolutely gutted about that.”