We analyze the stellar kinematics of 39 dwarf early-type galaxies (dEs) in the Virgo Cluster. Based on the specific stellar angular momentum λRe and the ellipticity, we find 11 slow rotators and 28 fast rotators. The fast rotators in the outer parts of the Virgo Cluster rotate significantly faster than fast rotators in the inner parts of the cluster. Moreover, 10 out of the 11 slow rotators are located in the inner 3° (D < 1 Mpc) of the cluster. The fast rotators contain subtle disk-like structures that are visible in high-pass filtered optical images, while the slow rotators do not exhibit these structures. In addition, two of the dEs have kinematically decoupled cores and four more have emission partially filling in the Balmer absorption lines. These properties suggest that Virgo Cluster dEs may have originated from late-type star-forming galaxies that were transformed by the environment after their infall into the cluster. The correlation between λRe and the clustercentric distance can be explained by a scenario where low luminosity star-forming galaxies fall into the cluster, their gas is rapidly removed by ram-pressure stripping, although some of it can be retained in their core, their star formation is quenched but their stellar kinematics are preserved. After a long time in the cluster and several passes through its center, the galaxies are heated up and transformed into slow rotating dEs.