Catalysis of the reactions: peptide-L-methionine + thioredoxin disulfide + H2O = peptide-L-methionine (S)-S-oxide + thioredoxin, and L-methionine + thioredoxin disulfide + H2O = L-methionine (S)-S-oxide + thioredoxin. Can act on oxidized methionine in peptide linkage with specificity for the S enantiomer. Thioredoxin disulfide is the oxidized form of thioredoxin.