Latos replaced Cueto, who threw just eight pitches before leaving with what initially was called back spasms but has since been described by the team as a mild right oblique strain.
Electing to start Leake means Cueto has been removed from the team's roster and can't return until the World Series, should the Reds advance that far.
The Reds lead the series 2-1 despite Tuesday's night's 10-inning loss. So far, the road team has won each game in the series.
Despite the uncertainty for Game 4, the Reds have gotten impressive pitching performances out of their starters in Games 2 and 3.
Bronson Arroyo allowed one hit over seven innings to win Game 2. Homer Bailey flirted with a no-hitter before earning a no-decision despite allowing one hit and one run while striking out 10 over seven innings in Game 3.