A reduced micromorphic model is formulated in the scope of crystal plasticity and crystalline cleavage damage. The finite strain formulation utilizes a single additional microvariable that is used to regularize localized inelastic deformation mechanisms. Damage is formulated as a strain-like variable to fit the generalized micromorphic microslip and/or microdamage based formulation. Strategies of treating slip and damage simultaneously and separately as non-local variables are investigated. The model accounts for size-effects that simultaneously affect the hardening behavior and allow to predict finite width damage localization bands. The results show that the micromorphic extension introduces extra-hardening in the vicinity of grain boundaries and slip localization zones in polycrystals. At the single crystal level slip band width is regularized. Two ways of dealing with damage localization were identified: An indirect method based on controlling width of slip bands that act as initiation sites for damage and a direct method in which damage flow is regularized together with or separately from plastic slip. Application to a real martensitic steel microstructure is investigated.