Age hardened aluminum alloys have superior strengths compared to non-age hardenable alloys due to the growth of a secondary phase of precipitates. This work presents a new crystal plasticity numerical framework to simulate the mechanical properties of precipitation-hardened aluminum alloys. A precipitation hardening constitutive law is implemented into the crystal plasticity finite element method (CPFEM) to simulate the localized deformation behavior of a commercially available AA6060-T6 extrusion. Experimental characterization in the form of uniaxial tension and cyclic simple shear is performed on the alloy of interest to validate the formulation. The framework uses information obtained from transmission electron microscopy (TEM) on a similar alloy for the simulation of the precipitate hardening response. This information is incorporated into an elastic-viscoplastic homogenization scheme to predict the behavior of the precipitate directly. The model is shown to capture the stress-strain response, precipitate anisotropy, and the observed Bauschinger effect with good agreement. A series of parametric analyses are then performed to show the effects of precipitation on the bulk and localized necking response. It is observed that the precipitate configuration heavily influences the polycrystalline behavior, and the localized behavior is also affected in a rather complex way. The model captures the general reduction of anisotropy in age-hardened alloys and serves as a good physics-based foundation for future investigative studies.