Context. Centaurus A (Cen A) is the closest radio-loud active galactic nucleus. Very Long Baseline Interferometry (VLBI) enables us to study the spectral and kinematic behavior of the radio jet¿counterjet system on milliarcsecond scales, providing essential information for jet emission and propagation models. Aims. In the framework of the TANAMI monitoring, we investigate the kinematics and complex structure of Cen A on subparsec scales. We have been studying the evolution of the central parsec jet structure of Cen A for over 3.5 years. The proper motion analysis of individual jet components allows us to constrain jet formation and propagation and to test the proposed correlation of increased high-energy flux with jet ejection events. Cen A is an exceptional laboratory for such a detailed study because its proximity translates to unrivaled linear resolution, where one milliarcsecond corresponds to 0.018 pc. Methods. As a target of the southern-hemisphere VLBI monitoring program TANAMI, observations of Cen A are done approximately every six months at 8.4 GHz with the Australian Long Baseline Array (LBA) and associated telescopes in Antarctica, Chile, New Zealand, and South Africa, complemented by quasi-simultaneous 22.3 GHz observations. Results. The first seven epochs of high-resolution TANAMI VLBI observations at 8.4 GHz of Cen A are presented, resolving the jet on (sub-)milliarcsecond scales. They show a differential motion of the subparsec scale jet with significantly higher component speeds farther downstream where the jet becomes optically thin. We determined apparent component speeds within a range of 0.1c to 0.3c and identified long-term stable features. In combination with the jet-to-counterjet ratio, we can constrain the angle to the line of sight to theta approx 12deg-45deg. Conclusions. The high-resolution kinematics are best explained by a spine-sheath structure supported by the downstream acceleration occurring where the jet becomes optically thin. On top of the underlying, continuous flow, TANAMI observations clearly resolve individual jet features. The flow appears to be interrupted by an obstacle causing a local decrease in surface brightness and circumfluent jet behavior. We propose a jet-star interaction scenario to explain this appearance. The comparison of jet ejection times to high X-ray flux phases yields a partial overlap of the onset of the X-ray emission and increasing jet activity, but the limited data do not support a robust correlation.