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Surface wrinkling provides an approach to fabricate micron and sub-micron-level biomaterial topographies that can mimic features of the dynamic, in vivo cell environment and guide cell adhesion, alignment, and differentiation. Most wrinkling research to date has used planar, two-dimensional (2D) substrates, and wrinkling work on three-dimensional (3D) structures has been limited. To enable wrinkle formation on architecturally complex, biomimetic 3D structures, here, we report a simple, low-cost experimental wrinkling approach that combines natural silk fibroin films with a recently developed advanced manufacturing technique for programming strain in complex 3D shape–memory polymer (SMP) scaffolds. By systematically investigating the influence of SMP programmed strain magnitude, silk film thickness, and aqueous media on wrinkle morphology and stability, we reveal how to generate and tune silk wrinkles on the micron and sub-micron scale. We find that increasing SMP programmed strain magnitude increases wavelength and decreases amplitudes of silk wrinkled topographies, while increasing silk film thickness increases wavelength and amplitude. Silk wrinkles persist after 24 h in cell culture medium. Wrinkled topographies demonstrate high cell viability and attachment. These findings suggest the potential for fabricating biomimetic cellular microenvironments that can advance understanding and control of cell–material interactions in engineering tissue constructs.