Catalyzes the reduction of methionine sulfoxide (MetSO) to methionine in proteins. Plays a protective role against oxidative stress by restoring activity to proteins that have been inactivated by methionine oxidation. Prevents the methionine sulfoxidation of the heat shock protein HSP21 and its subsequent inactivation. MSRA family specifically reduces the MetSO S-enantiomer. [thioredoxin]-disulfide + H2O + L-methionyl-[protein] = [thioredoxin]-dithiol + L-methionyl-(S)-S-oxide-[protein] [thioredoxin]-disulfide + H2O + L-methionine = [thioredoxin]-dithiol + L-methionine (S)-S-oxide Optimum pH is 8.0. Expressed in rosette and cauline leaves, and at lower levels in stems and flowers (at protein level). By light in etiolated seedlings (at protein level). Belongs to the MsrA Met sulfoxide reductase family.