He took part in the warm-up but left the field holding his back.
Danny Ward, of Liverpool, will replace Hennessey, starting the biggest game of his career after making his debut only in March.
Midfielder Joe Ledley, who broke a leg just five weeks ago, is fit to be among the substitutes but Dave Edwards will start alongside Joe Allen as the other holding player.
Slovakia's coach Jan Kozak has developed a settled side, which recently won 3-1 away to world champions Germany.
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They also lack a prolific striker, however, and are relying today on Michal Duris rather than Adam Nemec.
Both teams rely heavily on one player, Wales looking to their totem Gareth Bale while Napoli's Marek Hamsik will direct operations from midfield for Slovakia.
(Reporting by Steve Tongue; Editing by Ian Chadband)
