We present a 17-point map of the M17SW cloud core in the 1_{10}-1_{01} transition of ortho-water at 557 GHz obtained with the Submillimeter Wave Astronomy Satellite. Water emission was detected in 11 of the 17 observed positions. The line widths of the water emission vary between 4 and 9 km s^{-1}, and are similar to other emission lines that arise in the M17SW core. A direct comparison is made between the spatial extent of the water emission and the ^{13}CO J = 5\to4 emission; the good agreement suggests that the water emission arises in the same warm, dense gas as the ^{13}CO emission. A spectrum of the H_2^{18}O line was also obtained at the center position of the cloud core, but no emission was detected. We estimate that the average abundance of ortho-water relative to H_2 within the M17 dense core is approximately 1x10^{-9}, 30 times smaller than the average for the Orion core. Toward the H II region/molecular cloud interface in M17SW the ortho-water abundance may be about 5 times larger than in the dense core.