In this study, we developed a repeatable in vitro micropropagation protocol for the medicinal plant Asparagus cochinchinensis, based on indirect organogenesis using leaf segments cut from seedlings of in vitro-germinated seeds. We obtained 85% callus induction from the leaf segments within 4–5 weeks when grown on Murashige and Skoog (MS) medium supplemented with benzylaminopurine (BAP, 1.0 mg/L) and 1-naphthaleneacetic acid (NAA, 0.5 mg/L). We found that MS media supplemented with Kn (1.0 mg/L) in combination with NAA (1.0 mg/L) and BAP (1.0 mg/L) combined with NAA (0.5 mg/L) were the most effective in promoting shoot regeneration, yielding plantlets with 6.72 and 6.48 shoots per culture, respectively. When cultured on PGR-free half-strength MS medium, regenerated plants developed root systems with an average 11.0 roots per shoot cluster and an average length of 36.14 mm at 9 weeks. During acclimatization, regenerated plantlets showed 96.4% survival and exhibited normal growth characteristics and morphology. We also made an attempt to directly regenerate A. cochinchinensis from shoot apices but it was futile. Histological analyses revealed the presence of crystal idioblasts in young leaves from the early stages of leaf differentiation. The leaf-based plant regeneration technique developed herein could be employed for large-scale propagation of the plants over a short time period, thereby substantially contributing to the germplasm preservation and rapid propagation of A. cochinchinensis.