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With one set apiece, Marchenko was 5-0 ahead in the third before the Frenchman bowed out, having suffered an elbow injury earlier in the match.
Monfils, who reached the quarter-finals last year, inflicted a break of serve in the third and seventh games en route to a 6-2 first-set lead.
He then slipped on the baseline and landed on his elbow as Marchenko broke serve to move 3-1 ahead in the second - and he would not be caught.
The Ukrainian levelled up the match by winning the second set 6-4, and then moved one game away from the lead before his opponent retired.
Monfils was the fifth player to retire from round one.