Engaging functional biomaterial scaffolds to regulate stem cell differentiation has drawn a great deal of attention in the tissue engineering and regenerative medicine community. In this study, biomimetic composite nanofibrous scaffolds of hydroxyapatite/chitosan (HAp/CTS) were prepared to investigate their capacity for inducing murine mesenchymal stem cells (mMSCs) to differentiate into the osteogenic lineage, in the absence and presence of an osteogenic supplementation (i.e., ascorbic acid, β-glycerol phosphate, and dexamethasone), respectively. Using electrospun chitosan (CTS) nanofibrous scaffolds as the control, cell morphology, growth, specific osteogenic genes expression, and quantified proteins secretion on the HAp/CTS scaffolds were sequentially examined and assessed. It appeared that the HAp/CTS scaffolds supported better attachment and proliferation of the mMSCs. Most noteworthy was that in the absence of the osteogenic supplementation, expression of osteogenic genes including collagen I (Col I), runt-related transcription factor 2 (Runx2), alkaline phosphatase (ALP), and osteocalcin (OCN) were significantly upregulated in mMSCs cultured on the HAp/CTS nanofibrous scaffolds. Also increased secretion of the osteogenesis protein markers of alkaline phosphatase and collagen confirmed that the HAp/CTS nanofibrous scaffold markedly promoted the osteogenic commitment in the mMSCs. Moreover, the presence of osteogenic supplementation proved an enhanced efficacy of mMSC osteogenesis on the HAp/CTS nanofibrous scaffolds. Collectively, this study demonstrated that the biomimetic nanofibrous HAp/CTS scaffolds could support and enhance the adhesion, proliferation, and particularly osteogenic differentiation of the mMSCs. It also substantiated the potential of using biomimetic nanofibrous scaffolds of HAp/CTS for functional bone repair and regeneration applications.