We performed Herschel HIFI, PACS and SPIRE observations towards the molecular cloud interacting supernova remnant G349.7+0.2. An extremely broad emission line was detected at 557 GHz from the ground state transition 1_{10}-1_{01} of ortho-water. This water line can be separated into three velocity components with widths of 144, 27 and 4 km/s. The 144 km/s component is the broadest water line detected to date in the literature. This extremely broad line width shows importance of probing shock dynamics. PACS observations revealed 3 additional ortho-water lines, as well as numerous high-J carbon monoxide (CO) lines. No para-water lines were detected. The extremely broad water line is indicative of a high velocity shock, which is supported by the observed CO rotational diagram that was reproduced with a J-shock model with a density of 10^4 cm^{-3} and a shock velocity of 80 km/s. Two far-infrared fine-structure lines, [O~I] at 145 micron and [C~II] line at 157 micron, are also consistent with the high velocity J-shock model. The extremely broad water line could be simply from short-lived molecules that have not been destroyed in high velocity J-shocks; however, it may be from more complicated geometry such as high-velocity water bullets or a shell expanding in high velocity. We estimate the CO and H2O densities, column densities, and temperatures by comparison with RADEX and detailed shock models. Detection of Extremely Broad Water Emission from the molecular cloud interacting Supernova Remnant G349.7+0.2