The former world number one had hoped to build on the momentum that had carried him into the quarter-finals of the Citi Open before he pulled out of the Washington tournament citing fatigue.
But it was Pouille, world ranked number 17, who proved to be the more resourceful as he claimed his first win in five tries against Murray.
Murray, whose ranking plummeted into the 800s last month but has now risen to 375, has now fallen at the first hurdle in two of the four tournaments he has contested this year.
Spain's Pablo Carreno Busta, Britain's Kyle Edmund and Japan's Kei Nishikori also were early first round winners.
The 13th seeded Carreno Busta outlasted France's Richard Gasquet 6-3 2-6 6-3, 14th seeded Edmund beat American wildcard Mackenzie McDonald 6-3 6-2 and Nishikori turned back Russia's Andrey Rublev 7-5 6-3.
The tournament lost its top seed when Spanish world number one Rafael Nadal withdrew after winning the Rogers Cup on Sunday.
World number two Roger Federer, who skipped the Toronto event, is now the highest seed in Cincinnati.
(Reporting by Gene Cherry in Raleigh, North Carolina, editing by Pritha Sarkar)
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