We report integral-field spectroscopic observations with the Cambridge Infrared Panoramic Survey Spectrograph (CIRPASS) mounted on the Gemini South telescope of the nucleus of the nearby galaxy NGC 5128 (Centaurus A). We detect two-dimensional distributions of the following emission lines: [P ii], [Fe ii] and Paschen β. We compare our observations with previously published radio observations using the Very Large Array (VLA) and archival space-based near-infrared imaging using the Hubble Space Telescope (HST/NICMOS) and find similar features, as well as a region of high continuum coinciding with the jet (and its N1 knot) at about 2 arcsec north-east of the nucleus, possibly related to jet-induced star formation. We use the [Fe ii]/[P ii] ratio to probe the ionization mechanism, which suggests that with increasing radius shocks play an increasingly important role. We extract spatially resolved 2D kinematics of Paβ and [Fe ii] emission lines. All emission-line regions are part of the same kinematic structure which shows a twist in the zero-velocity curve beyond ∼1 arcsec (for both Paβ and [Fe ii]). The kinematics of the two emission lines are similar, but the Paβ velocity gradient is steeper in the centre while the velocity dispersion is low everywhere. The velocity dispersion of the [Fe ii] emission is relatively high featuring a plateau, approximately oriented in the same way as the central part of the warped disc. We use 2D kinematic information to test the hypothesis that the ionized gas is distributed in a circularly rotating disc. Assuming simple disc geometry we estimate the mass of the central black hole using Paβ kinematics, which is consistent with being distributed in a circularly rotating disc. We obtain M•= 8.25+2.25−4.25× 107 M⊙, for PA =−3° and i= 25°, excluding the M•–σ relation prediction at a 3σ confidence level, which is in good agreement with previous studies.