Russian Medvedev was chasing a second title in Dubai after he beat Felix Auger-Aliassime in the last four, and the former world number one reached the final without dropping a set.
Griekspoor said after his straight-sets win over Andrey Rublev that he was struggling with a hamstring injury and would have retired had he lost the second set.
"Not how I want to win a final. Hoping the injury for Griekspoor is not too bad and wishing him a speedy recovery," Medvedev wrote on X.