The Indo-Canadian pair suffered a 5-7, 5-7 defeat to Dutch Jean-Julien Rojer and Romania's Horea Tecau in the last-eight match which lasted one hour and 26 minutes on Monday.
Bopanna and Shapovalov had stunned sixth seed Kevin Kraweitz and Andreas Miles in the 2nd round to reach the last 8.
It was also Bopanna's best performance at a Slam since he made the quarterfinals at both the US Open and the French Open in 2018.
Earlier in the competition, India's top-ranked men's singles player, Sumit Nagal exit the tournament in the 2nd round after a defeat to Dominic Thiem.