Edmund called on the trainer while trailing 7-6(3) 6-3 2-1 and after a short discussion, he informed the umpire he was unable to continue.
Cuevas will next play Austrian fourth seed Dominic Thiem.
Edmund's exit left women's 26th seed Johanna Konta as the only Briton left in the singles competition.
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(Reporting by Sudip Kar-Gupta, editing by Pritha Sarkar)
