Diabetes mellitus is a chronic hormonal and metabolic disorder in which our body cannot generate necessary insulin or does not act in response to it, accordingly, ensuing in discordantly high blood sugar (glucose) levels. Diabetes mellitus can lead to systemic dysfunction in the multiorgan system, including cardiac dysfunction, severe kidney disease, lowered quality of life, and increased mortality risk from diabetic complications. To uncover possible therapeutic targets to treat diabetes mellitus, the in silico drug design technique is widely used, which connects the ligand molecules with target proteins to construct a protein-ligand network. To identify new therapeutic targets for type 2 diabetes mellitus, Azadirachta indica is subjected to phytochemical screening using in silico molecular docking, pharmacokinetic behavior analysis, and simulation-based molecular dynamic analysis. This study has analyzed around 63 phytochemical compounds, and the initial selection of the compounds was made by analyzing their pharmacokinetic properties by comparing them with Lipinski’s rule of 5. The selected compounds were subjected to molecular docking. The top four ligand compounds were reported along with the control drug nateglinide based on their highest negative molecular binding affinity. The protein-ligand interaction of selected compounds has been analyzed to understand better how compounds interact with the targeted protein structure. The results of the in silico analysis revealed that 7-Deacetyl-7-oxogedunin had the highest negative docking score of −8.9 Kcal/mol and also demonstrated standard stability in a 100 ns molecular dynamic simulation performed with insulin receptor ectodomain. It has been found that these substances may rank among the essential supplementary antidiabetic drugs for treating type 2 diabetes mellitus. It is suggested that more in vivo and in vitro research studies be carried out to support the conclusions drawn from this in silico research strategy.