Warrior Wellness Act This bill directs the Department of Defense (DOD) to report to congressional committees on its shortage of mental health providers and include a strategy to better recruit and retain mental health providers. DOD must report on the practices for prescribing medication during a specified period that were inconsistent with the post-traumatic stress disorder medication guidelines developed by DOD and the Veterans Health Administration (VHA). The Departments of the Army, Navy, and Air Force must each establish a monitoring program to (1) periodically review the medication prescribing practices of providers and report the results to DOD and the VHA, and (2) establish procedures to address prescribing practices that are inconsistent with post-traumatic stress disorder medication guidelines developed by the departments.