In this study, the click chemistry between N‐propargyl derivatives of substituted 4H‐pyrano[2,3‐d]pyrimidines and tetra‐O‐acetyl‐α‐d‐glucopyranosyl azide carried out under catalytic conditions using catalyst CuI@Montmorillonite and additive N,N‐diisopropylethylamine (DIPEA). The yields of obtained hybrid compounds having 4H‐pyrano[2,3‐d]pyrimidine connected to 1H‐1,2,3‐triazole rings were about 85–94 %. All these synthesized hybrid compounds were examined for in vitro α‐amylase (with IC50 values in the range of 103.63±1.13 μM to 295.45±1.11 μM) and α‐glucosidase (with IC50 values in the range of 45.63±1.14 μM to 184.52±1.15) inhibitory activity. Amongst this series, ethyl ester 8m showed the best inhibitory activity against α‐amylase with IC50 of 103.63±1.13 μM, while ethyl ester 8t exhibited the highest activity against α‐glucosidase with IC50 of 45.63±1.14 μM. The kinetics of the inhibition of compound 8t showed the competitive α‐glucosidase inhibitor property of this compound. Furthermore, the most potent compounds had any cytotoxicity against human normal cells. Induced fit docking and molecular dynamics simulation calculations indicated that the inhibition potential compounds 8m and 8t had the active interactions with the residues in receptors of corresponding tested enzymes. The calculated binding free energy from MM‐GBSA approach showed that the major energy components contributed to the active binding of these studied inhibitors, including Coulomb, lipophilic and van der Waals energy. Further, 300 ns MD simulation showed that studied ligand‐protein complexes were stable and indicated the structural observations into mode of binding in these complexes.