Tendon and ligament (T/L) injuries present an important clinical challenge due to their intrinsically poor healing capacity. Natural healing typically leads to the formation of scar-like tissue possessing inferior mechanical properties. Therefore, tissue engineering has gained considerable attention as a promising alternative for T/L repair. In this study, we fabricated braided nanofibrous scaffolds (BNFSs) as a potential construct for T/L tissue engineering. Scaffolds were fabricated by braiding 3, 4, or 5 aligned bundles of electrospun poly(L-lactic acid) nanofibers, thus introducing an additional degree of flexibility to alter the mechanical properties of individual scaffolds. We observed that the Young's modulus, yield stress, and ultimate stress were all increased in the 3-bundle compared to the 4- and 5-bundle BNFSs. Interestingly, acellular BNFSs mimicked the normal tri-phasic mechanical behavior of native tendon and ligament (T/L) during loading. When cultured on the BNFSs, human mesenchymal stem cells (hMSCs) adhered, aligned parallel to the length of the nanofibers, and displayed a concomitant realignment of the actin cytoskeleton. In addition, the BNFSs supported hMSC proliferation and induced an upregulation in the expression of key pluripotency genes. When cultured on BNFSs in the presence of tenogenic growth factors and stimulated with cyclic tensile strain, hMSCs differentiated into the tenogenic lineage, evidenced most notably by the significant upregulation of Scleraxis gene expression. These results demonstrate that BNFSs provide a versatile scaffold capable of supporting both stem cell expansion and differentiation for T/L tissue engineering applications.