Polylactic acid (PLA) is widely used in tissue engineering and other biomedical applications. PLA can be modified with appropriate biocompatible ceramic materials since this would allow tailoring the mechanical properties of the tissues to be engineered. In this study, PLA-based non-woven fibrillar nanocomposites containing nanoparticles of hydroxyapatite (HA), a bioceramic commonly used in bone tissue engineering, were prepared via solution blow spinning (SBS). The compositions of the final materials were selected to study the influence of HA concentration on the structure, morphology, and thermal and mechanical properties. The resulting materials were highly porous and mainly constituted fibers. FTIR analysis did not reveal any specific interactions. The diameters of the fibers varied very little with the composition. For example, slightly thinner fibers were obtained for pure PLA and PLA + 10% HA, with fiber diameters of less than 400 nm, while the thicker fibers were found for PLA + 1% HA, with average diameters of 427 ± 170 nm. The crystallinity and stiffness of the PLA/HA composite increased with the HA content. Further, composites containing PLA fibers with slightly larger diameters were more ductile. Thus, with an appropriate balance between factors, such as the diameter of the solution-blow-spun PLA fibers, HA particle content, and degree of crystallinity, PLA/HA composites may be effectively used in tissue engineering applications.