The detection of the 6.7 GHz line of methanol (CH3OH) is reported for the first time toward an object beyond the Magellanic Clouds. Using the Effelsberg 100 m telescope, two absorption features were identified toward the Seyfert 2 galaxy NGC 3079. Both components probably originated on lines-of-sight toward the central region, presumably absorbing the radio continuum of the nuclear sources A, B, and E of NGC 3079. One absorption feature, at the systemic velocity, is narrow and may arise from gas not related to the nuclear environment of the galaxy. The weaker blue-shifted component is wider and may trace outflowing gas. Total A-type CH3OH column densities are estimated to be between a few times 10^13 and a few times 10^15 cm^-2. Because of a highly frequency-dependent continuum background, the overall similarity of HI, OH, and CH3OH absorption profiles hints at molecular clouds that cover the entire area occupied by the nuclear radio continuum sources ~ 4 pc.