Britain's two-time Wimbledon champion, still working his way back to form after undergoing hip surgery two years ago, went down 7-6 (8) 6-1.
Murray, who was unable to compete at the Australian Open after testing positive for Covid-19 in January, instead played at a lower-level Challenger tournament in Italy where he reached the final before heading to France.
The 33-year-old Scot may not get the court-time in his legs that he wanted this week, but he certainly got a work-out in a first set lasting an hour and 10 minutes against Belarusian Gerasimov.
Murray fell behind to an early break of serve but hit back to level the set at 4-4.
A double-fault gifted Gerasimov a mini-break in the tie-break and although Murray saved three set points, his opponent converted a fourth with an ace.
The second set was, by contrast, a one-sided affair with Murray winning just two points on serve as Gerasimov raced into a 5-0 lead.
Murray saved a match point as he finally got on the board but it was just delaying the inevitable as Gerasimov sent the former world number one tumbling out.