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We endow the diffeomorphism group $Dif{f}_{Orb}(Q,)$ of a paracompact (reduced) orbifold with the structure of an infinite-dimensional Lie group modeled on the space of compactly supported sections of the tangent orbibundle. For a second countable orbifold, we prove that $Dif{f}_{Orb}(Q,)$ is C⁰-regular, and thus regular in the sense of Milnor. Furthermore, an explicit characterization of the Lie algebra associated to $Dif{f}_{Orb}(Q,)$ is given.