Konta, 25, lost 6-4 6-3 to Slovakian qualifier and world number 121 Kristina Kucova on Friday in Montreal, Canada.
A win for Konta, ranked 147th last June, would have made her the first British woman since Jo Durie in September 1984 to make the WTA top 10.
Kucova, 26, will play American 10th seed Madison Keys in the semi-final.
Romanian Simona Halep and Australian Open champion Angelique Kerber of Germany will meet in the other semi-final.
The surprise defeat for Konta comes a week after she claimed her first WTA Tour title in California, and in a year that has seen her reach a Grand Slam semi-final in Australia.
She had won seven matches in a row before meeting Kucova, having gone on a 16-match winning streak during the North American hard-court season in 2015.
Kucova said: "I cannot believe it - I'm so happy. There is no secret to my success. I feel so good here. I get so much energy from the crowd."
Johanna Konta missed a chance to become the first British woman to break into the world's top 10 for 32 years with a Rogers Cup quarter-final defeat.