Military Energy Security Act of 2022 This bill requires the Department of Defense (DOD) to set a goal to eliminate the use of Russian energy on each main operating base in the area of responsibility of the U.S. European Command (USEUCOM) not later than five years after the implementation of an installation energy plan for each base. Under the bill, DOD must submit to Congress (1) a list of main operating bases within the area of responsibility of USEUCOM ranked according to mission criticality and vulnerability to energy disruption, (2) an installation energy plan for each base on the list, and (3) an assessment of the feasibility of reaching the goal for the elimination of the use of Russian energy on each base. DOD must begin implementing plans not later than 30 days after submitting the plans to Congress. Additionally, DOD must establish a policy to ensure that any new military base in the area of responsibility of USEUCOM is established to include the consideration of energy security, energy resilience, and mitigation of risk due to energy disruption. DOD must annually brief Congress on the installation energy plans.