Tissue engineering seeks to repair or regenerate tissues through combinations of implanted cells, biomaterial scaffolds and biologically active molecules. The rapid restoration of tissue biomechanical function remains an important challenge, emphasizing the need to replicate structural and mechanical properties using novel scaffold designs. Here we present a microscale 3D weaving technique to generate anisotropic 3D woven structures as the basis for novel composite scaffolds that are consolidated with a chondrocyte-hydrogel mixture into cartilage tissue constructs. Composite scaffolds show mechanical properties of the same order of magnitude as values for native articular cartilage, as measured by compressive, tensile and shear testing. Moreover, our findings showed that porous composite scaffolds could be engineered with initial properties that reproduce the anisotropy, viscoelasticity and tension-compression nonlinearity of native articular cartilage. Such scaffolds uniquely combine the potential for load-bearing immediately after implantation in vivo with biological support for cell-based tissue regeneration without requiring cultivation in vitro.