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We analyze the dynamics of the Sun-Earth-Moon system in the context of aparticular class of theories of gravity where curvature and matter arenonminimally coupled (NMC). These theories can potentially violate theEquivalence Principle as they give origin to a fifth force and a extranon-Newtonian force that may imply that Earth and Moon fall differently towardsthe Sun. We show, through a detailed analysis, that consistency with the boundon Weak Equivalence Principle arising from 48 years of Lunar Laser Rangingdata, for a range of parameters of the NMC gravity theory, can be achieved viathe implementation of a suitable screening mechanism.

Equivalence principle violation in nonminimally coupled gravity and constraints from Lunar Laser Ranging