We observed multiple CO transition lines and the HCN(1-0) line at ~ 1" (~ 34 pc) or higher resolution toward the Seyfert 2 nucleus of M51 using the IRAM Plateau de Bure Interferometer (PdBI) and the Submillimeter Array (SMA). All the images show very similar overall molecular gas distribution; there are two discrete clouds at the eastern and western sides of the nucleus, and the western cloud exhibits an elongated distribution and velocity gradient along the radio jet. In addition, high HCN(1-0)/CO(1-0) brightness temperature ratios of about unity have been observed, especially along the radio jet, similar to those observed in shocked molecular gas in our Galaxy. This strongly indicates that the molecular gas along the jet is shocked, that the radio jet and the molecular gas are interacting, and the jet is entraining both diffuse (CO) and dense (HCN) molecular gas outwards from the circumnuclear region. This is the first clear imaging of the out owing molecular gas entrained by the AGN jet, and showing the detailed physical status of out owing molecular gas. Since a relatively high HCN(1-0)/CO(1-0) ratio has been observed in the high velocity wing of ultraluminous infrared galaxies, it can also be explained by a similar mechanism to those we describe here.