Histone deacetylases (HDACs) are essential epigenetic regulators, with HDAC6 overexpression linked to estrogen receptor (ER) activity and breast cancer progression. While several HDAC6 inhibitors have been investigated, their clinical success remains limited due to toxicity and off-target effects, necessitating the discovery of novel, selective inhibitors. This study employs a multi-stage computational approach to identify potent HDAC6 inhibitors for breast cancer therapy. A large-scale virtual screening of 264 834 compounds was conducted, followed by molecular docking, molecular dynamics (MD) simulations (100 ns), molecular mechanics/generalized born surface area (MM/GBSA) binding free energy calculations, and absorption, distribution, metabolism, excretion, and toxicity (ADMET) predictions. The HDI-3 emerged as the most promising candidate among replicate simulations, exhibiting a substantially favorable MM/GBSA binding free energy of −130.67 kcal/mol—indicative of strong thermodynamic stability and stronger binding affinity compared to reference inhibitors Trichostatin A and Ricolinostat. Molecular dynamics simulations revealed that HDI-3 maintained structural stability, persistent key interactions with active site residues (ASP649, HIS651, ASP742), and low conformational fluctuations. The ADMET evaluation confirmed HDI-3’s favorable pharmacokinetic properties, including optimal bioavailability, non-mutagenicity, and low hepatotoxicity. Essential dynamics and principal component analysis further validated its stable binding profile. While these findings highlight HDI-3 as a selective and pharmacologically viable HDAC6 inhibitor, it is important to acknowledge that the results are entirely computational. Therefore, experimental validation is essential to confirm the compound’s efficacy and safety. This integrated computational pipeline provides an efficient strategy to accelerate targeted drug discovery, laying the groundwork for future experimental investigations.