The new and distinct cultivar of perennial Salvia plant named ‘Moulin Rouge’ characterized by its large, deep rosy-pink flowers from dark deep-rose buds and calyxes, densely arranged in verticils. The new plant has a medium height, compact, rounded habit with stiff, upright, heavily-branched stems and a strong vigorous growth rate and dark gray-green foliage. ‘Moulin Rouge’ is useful for landscaping as a specimen plant or en masse.