The methanol molecule CH _ { 3 } OH has a complex microwave spectrum with a large number of very strong lines .
This spectrum includes purely rotational transitions as well as transitions with contributions of the internal degree of freedom associated with the hindered rotation of the OH group .
The latter takes place due to the tunneling of hydrogen through the potential barriers between three equivalent potential minima .
Such transitions are highly sensitive to changes in the electron-to-proton mass ratio , \mu = m _ { e } / m _ { p } , and have different responses to \mu -variations .
The highest sensitivity is found for the mixed rotation-tunneling transitions at low frequencies .
Observing methanol lines provides more stringent limits on the hypothetical variation of \mu than ammonia observation with the same velocity resolution .
We show that the best quality radio astronomical data on methanol maser lines constrain the variability of \mu in the Milky Way at the level of | \Delta \mu / \mu| < 28 \times 10 ^ { -9 } ( 1 \sigma ) which is in line with the previously obtained ammonia result , | \Delta \mu / \mu| < 29 \times 10 ^ { -9 } ( 1 \sigma ) .
This estimate can be further improved if the rest frequencies of the CH _ { 3 } OH microwave lines will be measured more accurately .