Context. Polarization of maser emission contains unique information on the magnetic field in the densest regions of massive star formation. Aims. Magnetic field induced Zeeman-splitting has been measured for the strongest known 6.7 GHz methanol maser, which arises in the massive star-forming region G09.62+0.20. This maser is one of a handful of periodically flaring methanol masers. Magnetic field measurements can possibly provide insights into the elusive mechanism responsible for this periodicity. Methods. The 100-m Effelsberg telescope was used to monitor the 6.7 GHz methanol masers of G09.62+0.20, in weekly intervals, for just over a two-month period during which one of the maser flares occurred. Results. With the exception of a two-week period during the peak of the maser flare, we measure a constant magnetic field of B || ≈ 11 ± 2 mG in the two strongest maser components of G09.62+0.20 that are separated by more than 200 AU. In the two-week period coinciding exactly with the peak of the maser flare of the strongest maser feature, we measure a sharp decrease and possible reversal of the Zeeman-splitting. Conclusions. While the two phenomena are clearly related, the Zeeman-splitting decrease occurs only close to the flare maximum. Intrinsic magnetic field variability is thus unlikely to be the reason for the maser variability. The exact cause of both variabilities is still unclear, but it could be related to either background amplification of polarized emission or the presence of a massive protostar with a close-by companion. However, the variability in the splitting between the right-and left-circular polarizations could also be caused by non-Zeeman effects related to the radiative transfer of polarized maser emission. In this case we can place limits on the magnetic field orientation and the maser saturation level.