Background: This study began with a search in three databases, totaling six libraries (ChemBridge-DIVERSet, ChemBridge-DIVERSet-EXP, Zinc_Drug Database, Zinc_Natural_Stock, Zinc_FDA_BindingDB, Maybridge) with approximately 2.5 million compounds with the aim of selecting potential inhibitors with antiproliferative activity on the chimeric tyrosine kinase encoded by the BCR-ABL gene. Methods: Through hierarchical biochemoinformatics, ADME/Tox analyses, biological activity prediction, molecular docking simulations, synthetic accessibility and theoretical synthetic routes of promising compounds and their lipophilicity and water solubility were realized. Results: Predictions of toxicological and pharmacokinetic properties (ADME/Tox) using the top100/base (600 structures), in comparison with the commercial drug imatinib, showed that only nine exhibited the desired properties. In the prediction of biological activity, the results of the nine selected structures ranged from 13.7% < Pa < 65.8%, showing them to be potential protein kinase inhibitors. In the molecular docking simulations, the promising molecules LMQC01 and LMQC04 showed significant values in molecular targeting (PDB 1IEP—resolution 2.10 Å). LMQC04 presented better binding affinity (∆G = −12.2 kcal mol−1 with a variation of ±3.6 kcal mol−1) in relation to LMQC01. The LMQC01 and LMQC04 molecules were advanced for molecular dynamics (MD) simulation followed by Molecular Mechanics with generalized Born and Surface Area solvation (MM-GBSA); the comparable, low and stable RMSD and ΔE values for the protein and ligand in each complex suggest that the selected compounds form a stable complex with the Abl kinase domain. This stability is a positive indicator that LMQC01 and LMQC04 can potentially inhibit enzyme function. Synthetic accessibility (SA) analysis performed on the AMBIT and SwissADME webservers showed that LMQC01 and LMQC04 can be considered easy to synthesize. Our in silico results show that these molecules could be potent protein kinase inhibitors with potential antiproliferative activity on tyrosine kinase encoded by the BCR-ABL gene. Conclusions: In conclusion, the results suggest that these ligands, particularly LMQC04, may bind strongly to the studied target and may have appropriate ADME/Tox properties in experimental studies. Considering future in vitro or in vivo assays, we elaborated the theoretical synthetic routes of the promising compounds identified in the present study. Based on our in silico findings, the selected ligands show promise for future studies in developing chronic myeloid leukemia treatments.