The Australia Telescope Compact Array has been used to map the distribution of emission from the 6.7-GHz 5(1)-6(0)A(+) transition of methanol over the HII region/molecular cloud complex Sgr B2. Images obtained with restored beamwidths of 3 arcsec and lower reveal the presence of 11 methanol maser locations, seven of which are near maser positions for other molecules: Methanol absorption has been detected in two well-known clouds, with velocities near 65 and 80 km s(-1), which observations of other molecules have shown to be associated with Sgr B2. Although other transitions, including the 2(0)-3(-1)E transition of methanol at 12.2 GHz, have shown that the 65 km s(-1) cloud extends over all the continuum emission, the 6.7-GHz absorption is confined to the north and west, with optical depths of around unity. No absorption was found to be associated with a third known cloud with a velocity near 50 km s(-1). We suggest that 6.7-GHz absorption occurs only in the regions of higher temperature in the molecular clouds. Assumed cloud temperatures of 20 K yield methanol column densities as high as 7.5 x 10(18) cm(-2).