Catalyzes the formation of N(5)-methyl-L-glutamine from glutamate and methylamine. ATP + L-glutamate + methylamine = ADP + H(+) + N(5)-methyl-L-glutamine + phosphate No activity is detected with Mn(2+). Induced during growth on methylamine. Fails to grow on methylamine. N(5)-methyl-L-glutamine is not detected in the intracellular pool of free amino acids from the deletion mutant. Belongs to the glutamine synthetase family. Type 3 subfamily.