Andrographis paniculata (Burm.f.) Wall. (Acanthaceae) is revered for its medicinal properties. In vitro culture of medicinal plants has assisted in improving both the quantity and quality of their yield. The current study investigated the effects of different surface sterilization treatments, plant growth regulators (PGRs), and elicitors on culture establishment and axillary shoot multiplication of A. paniculata. Subsequently, the production of andrographolide in the in vitro plantlets was evaluated using high-performance liquid chromatography (HPLC) analysis. The shoot-tip explant was successfully sterilized using 60% commercial bleach for 5 min of immersion with a 90% survival rate and 96.67% aseptic culture. The optimal PGR for shoot growth was 6-benzylaminopurine (BAP) at 17.76 µM, supplemented into Murashige and Skoog (MS) media, producing 23.57 ± 0.48 leaves, 7.33 ± 0.10 shoots, and a 3.06 ± 0.02 cm length of shoots. Subsequently, MS medium supplemented with 5 mg/L chitosan produced 26.07 ± 0.14 leaves, 8.33 ± 0.07 shoots, and a 3.63 ± 0.02 cm length of shoots. The highest andrographolide content was obtained using the plantlets harvested from 5 mg/L chitosan with 2463.03 ± 0.398 µg/mL compared to the control (without elicitation) with 256.73 ± 0.341 µg/mL (859.39% increase). The results imply that the protocol for the shoot-tip culture of A. paniculata was developed, and that elicitation enhanced the herbage yield and the production of andrographolide.