A series of novel naphthopyrano[2,3-d]pyrimidin-11(12H)-one containing isoxazole nucleus 4 was synthesized under microwave irradiation and classical conditions in moderate to excellent yields upon 1,3-dipolar cycloaddition reaction using various arylnitrile oxides under copper(I) catalyst. A one-pot, three-component reaction, N-propargylation and Dimroth rearrangement were used as the key steps for the preparation of the dipolarophiles3. The structures of the synthesized compounds were established by 1H NMR, 13C NMR and HRMS-ES means. The present study aims to also predict the theoretical assembly of the COVID-19 protease (SARS-CoV-2 Mpro) and to discover in advance whether this protein can be targeted by the compounds 4a–1 and thus be synthesized. The docking scores of these compounds were compared to those of the co-crystallized native ligand inhibitor (N3) which was used as a reference standard. The results showed that all the synthesized compounds (4a–l) gave interesting binding scores compared to those of N3 inhibitor. It was found that compounds 4a, 4e and 4i achieved greatly similar binding scores and modes of interaction than N3, indicating promising affinity towards SARS-CoV-2 Mpro. On the other hand, the derivatives 4k, 4h and 4j showed binding energy scores (−8.9, −8.5 and −8.4 kcal/mol, respectively) higher than the Mpro N3 inhibitor (−7.0 kcal/mol), revealing, in their turn, a strong interaction with the target protease, although their interactions were not entirely comparable to that of the reference N3.