We report the detection of the Zeeman effect in the 44 GHz Class I methanol maser line toward the high mass star forming region DR21W. There are two prominent maser spots in DR21W at the ends of a northwest-southeast linear arrangement. For the maser at the northwestern end (maser A), we fit three Gaussian components. In the strongest component, we obtain a significant Zeeman detection, with $zB_{rm los}=-23.4pm3.2$ Hz. If we use $z=-0.920$ Hz mG$^{-1}$ for the $F=5 rightarrow 4$ hyperfine transition, this corresponds to a magnetic field $|B_{rm los}|=25.4$ mG; $B_{rm los}$ would be higher if a different hyperfine was responsible for the 44 GHz maser, but our results also rule out some hyperfines, since fields in these regions cannot be hundreds of mG. Class I methanol masers form in outflows where shocks compress magnetic fields in proportion to gas density. Designating our detected $B_{rm los}=25$ mG as the magnetic field in the post-shock gas, we find that $B_{rm los}$ in the pre-shock gas should be 0.1-0.8 mG. Although there are no thermal-line Zeeman detections toward DR21W, such values are in good agreement with Zeeman measurements in the CN thermal line of 0.36 and 0.71 mG about $3.5$ away in DR21(OH) in gas of comparable density to the pre-shock gas density in DR21W. Comparison of our derived magnetic energy density to the kinetic energy density in DR21W indicates that magnetic fields likely play a significant role in shaping the dynamics of the post-shocked gas in DR21W.
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