Methionine-sulfoxide reductase that specifically reduces methionine (R)-sulfoxide back to methionine (By similarity). While in many cases, methionine oxidation is the result of random oxidation following oxidative stress, methionine oxidation is also a post-translational modification that takes place on specific residue (By similarity). [thioredoxin]-disulfide + H2O + L-methionyl-[protein] = [thioredoxin]-dithiol + L-methionyl-(R)-S-oxide-[protein] Binds 1 zinc ion per subunit. Belongs to the MsrB Met sulfoxide reductase family.