Bioinks play a central role in 3D-bioprinting by providing the supporting environment within which encapsulated cells can endure the stresses encountered during the digitally-driven fabrication process, and continue to mature, proliferate, and eventually form extracellular matrix (ECM). In order to be most effective, it is important that bioprinted constructs recapitulate the native tissue milieu as closely as possible. As such, musculoskeletal soft tissue constructs can benefit from bioinks that mimic their nanofibrous matrix constitution, which is also critical to their function. This study focuses on the development and proof-of-concept assessment of a fibrous bioink composed of alginate hydrogel, polylactic acid nanofibers and human adipose-derived stem cells (hASC) for bioprinting such tissue constructs. First, hASC proliferation and viability were assessed in 3D-bioplotted strands over 16 days in vitro. Then, a human medial knee meniscus digitally modeled using magnetic resonance images was bioprinted and evaluated over 8 weeks in vitro. Results show that the nanofiber-reinforced bioink allowed higher levels of cell proliferation within bioprinted strands, with a peak at day 7, while still maintaining a vast majority of viable cells at day 16. The cell metabolic activity on day 7 was 28.5% higher in this bioink compared to the bioink without nanofibers. Histology of the bioprinted meniscus at both 4 and 8 weeks showed 54% and 147% higher cell density, respectively, in external versus internal regions of the construct. Presence of collagen and proteoglycans was also noted in areas surrounding the hASC, indicating ECM secretion and chondrogenic differentiation.