We present a kinematical study of the ionized and molecular gas in the central region (∼7–14″∼100–200 pc) of the nearby radio galaxy Centaurus A (Cen A). We used JWST/MIRI MRS ∼5−28 μm observations taken as part of the Mid-Infrared Characterization of Nearby Iconic galaxy Centers (MICONIC) of the MIRI European Consortium. The two gas phases present contrasting morphologies and kinematics in Cen A. The brightest emission from the ionized gas, traced with a range of ionization potential (IP) lines analyzed here (from [Fe II] to [Ne VI]), is extended along the direction of the radio jet. We also detected emission from low IP emission lines and H2 transitions in the galaxy disk region mapped with MRS. Both gas phases present rotational motions in the disk but also complex kinematics. The MRS observations reveal several ionized gas kinematical features that are consistent with simulation predictions of a jet-driven bubble and outflow interacting with the galaxy interstellar medium. These include broad components in the nuclear line profiles (σ∼600 km s−1 in [Ar II] and [Ne III]), high velocities (reaching approximately +1000, −1400 km s−1) confined within the nuclear region, velocities of hundreds of kilometers per second in several directions in the central 2″, and enhanced velocity dispersions perpendicular to the radio jet. Moreover, we find evidence of shock excitation in the nuclear region of Cen A based on mid-infrared line ratios. We compared the ionized gas mass outflow rate with Cen A's active galactic nucleus (AGN) luminosity and radio jet power and demonstrate that both mechanisms provide sufficient energy to launch the outflow. The noncircular motions observed in the mid-infrared H2 lines can be reproduced with either a warped rotating disk model or a radial component. The latter might be to related to gas streamers detected in cold molecular gas. Notably, there is no clear indication of a fast nuclear H2 outflow in Cen A, only a weak blueshifted component in the line profiles. This could be due to a relatively low nuclear warm H2 column density and/or the limited geometrical coupling of Cen A's inner radio jet with the circumnuclear disk of the galaxy.