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 zBlos = −23.4 3.2 Hz. If we use z = −0.920 Hz mG−1 for the F = 5 → 4 hyperfine transition, this corresponds to a magnetic field, ; Blos would be higher if a different hyperfine were responsible for the 44 GHz maser, but our results also rule out some hyperfines, as 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 Blos = 25 mG as the magnetic field in the postshock gas, we find that Blos in the preshock 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 preshock gas density in DR21W. Comparison of our derived magnetic energy density with the kinetic energy density in DR21W indicates that magnetic fields likely play a significant role in shaping the dynamics of the postshocked gas in DR21W.