This study was conducted to develop a protocol for in vitro shoot multiplication and callus induction of various mung bean varieties to obtain enhanced phytochemical content with the help of elicitors. For shoot multiplication, two types of explants (shoot tips and nodal tips) of three varieties of mung bean (Mung NCM-13, MgAT-7, and MgAT-4) were used. Both types of explants from in vitro and in vivo sources were cultured on the MS medium supplemented with different concentrations (0.25–3.0 mg/L, increment of 0.5 mg/L) and combinations of BAP and IBA as independent treatments. For callus induction, leaf explants (in vitro source) were cultured on MS medium supplemented with 2,4-D (1–3 mg/L) alone or in combination with BAP or NAA (0.5 and 1.0 mg/L). For the enhanced production of phenolics and glycosides, calli were cultured on MS media supplemented with zinc oxide (0.5 mg/L) and copper oxide nanoparticles (0.5 mg/L) as nano-elicitors. Results showed that in vitro explants responded better in terms of shoot length, number of shoots, and number of leaves per explant when compared to in vivo explants. Moreover, shoot tips were better than nodal explants to in vitro culturing parameters. All three varieties showed the optimized results in the MS medium supplemented with 1 mg/L BAP, while roots were produced only in cultures fortified with 1 mg/L IBA. The leaf explants of in vitro and soil-grown plantlets showed a maximum callogenic response of 90 and 80%, respectively, on MS medium supplemented with 2,4-D (3 mg/ml). Maximum phenolic content (101.4 μg of gallic acid equivalent/g) and glycoside content (34 mg of amygdalin equivalent/g of plant material) was observed in the calli cultured on MS medium supplemented with 3 mg/L of 2,4-D. Furthermore, the addition of zinc oxide (0.5 mg/L) and copper oxide (0.5 mg/L) nanoparticles to the callus culture medium significantly enhanced the phenolic content of Mung NCM-13 (26%), MgAT-7 (25.6%), and MgAT-4 (22.7%). Glycosidic content was also found to be increased in Mung NCM-13 (50%), MgAT-7 (37.5%), and MgAT-4 (25%) varieties when compared to the control. It is suggested that elicitation of in vitro cultures of mung beans with nanoparticles could be an effective strategy for the enhanced production of secondary metabolites.