The former world number one had taken a week off in order to prepare for the Masters Series event, but the 31-year-old was edged out 6-1 1-6 6-4 by the 16th seed.
Murray struggled to find any rhythm on his serve during the opening set, and Pouille broke on three occasions to threaten a quick-fire victory.
However, the Scot responded by making light work of the second in order to set up a decider, only to fall a break of serve down early in the third.
Murray battled well to remain competitive, but Pouille proved too strong on his serve and was able to wrap up the win in one hour and 53 minutes.
The world number 375 will now look to prepare for the US Open at Flushing Meadows, which begins on August 27.