We report Hubble Space Telescope NICMOS observations of the central region of NGC 5128 at 2.2 mu m and in Pa alpha . The continuum images show extended emission typical of an elliptical galaxy and a strong unresolved central source we identify as the nucleus of the galaxy. Its position is consistent with ground-based IR and radio data, and with the peak of reddening found with the first wide field planetary camera. In Pa alpha , we detect a prominent elongated structure, centered on the nucleus, extended by ~=2"at a position angle of ~=33 deg, and with a major to minor axis ratio of ~2. We interpret this as an inclined, ~40 pc diameter, thin nuclear disk of ionized gas rather than a jet-gas cloud interaction. We do see several weaker Pa alpha features, some of which may be circumnuclear gas clouds shocked by the X-ray/radio jet. The disk is one of the smallest ever observed at the nucleus of an active galactic nucleus (AGN). It is not perpendicular to the jet but is consistent with being oriented along the major axis of the bulge. If it represents the warped outer portion of an accretion disk around a black hole, we conclude that even on the scale of a few parsecs, the disk is dominated by the galaxy gravitational potential and is not directly related to the symmetry axis of the AGN.