Hospitals face challenges to improve efficiency in order to meet an increasing demand for high quality of care and low costs. Industry-based methods such as lean healthcare (LH) are implemented to improve healthcare systems. This study presents a LH implementation following the DMAIC approach (Define-Measure-Analysis-Improve-Control) in a Mexican public hospital, and contributes to the literature by analyzing the relation of waste reduction and sustainability. We focused on improving the medical supply chain from a temporary warehouse (TW) to the operating room (OR). Therefore, we analyzed the value stream including main surgical procedures and their related medical supplies, and identified different causes of inefficiency, which were evaluated and controlled. As a result, five types of waste were reduced through different tools including: value stream map, Kanban, 5’s, among others. Over-processing requests were reduced 15.3%; similarly, defective identification numbers were reduced up to 46.5%, redundant processing was improved by 94.8%, unnecessary inventories were reduced near to 2.8% of the TW inventory, and transportation waste was reduced up to 16.7%. As a consequence, the lead-time for the main supplies was reduced 33 days. Results indicate that LH and DMAIC are effective to reduce waste and highly conducive to improve healthcare process sustainability.