Konta, the first British woman to reach the last eight of the tournament, was beaten 6-4 6-2 by her Belarusian opponent in just over 90 minutes.
World number eight Azarenka, 26, is on course for back-to-back titles after beating Serena Williams in Indian Wells earlier this month.
World number 23 Konta, 24, failed to convert any of her five break points.
The Briton, making her debut in Miami, would have broken into the world top 20 had she reached the final.
Azarenka, who won the tournament in 2009 and 2011, made just 14 unforced errors in 119 points.
She will next face either second-seeded German Angelique Kerber or American world number 22 Madison Keys.
