Context. Th 28 is a Classical T Tauri star in the Lupus 3 cloud that drives an extended bipolar jet. Previous studies of the inner jet identified signatures of rotation around the outflow axis, a key result for theories of jet launching. Thus this is an important source in which to investigate the poorly understood jet launching mechanism. Aims. In this study we investigate the morphology and kinematics of the Th 28 micro-jets, with the aim of characterising their structure and outflow activity, using optical integral-field spectroscopy observations obtained with VLT/MUSE. Methods. We use spectro-imaging and position–velocity maps to investigate the kinematic and morphological features of the jet and to obtain a catalogue of emission lines in which the jet is visible. A Lucy-Richardson deconvolution procedure is used to differentiate the structure of the inner micro-jet region in selected emission lines. Spatial profiles extracted perpendicular to the jet axis are fitted to investigate the jet width, opening angle, and the evolution of the jet axis. Results. We confirm the previously identified knot HHW2 within the red-shifted jet and identify three additional knots in each lobe for the first time. We also find [O III]λ5007 emission from the blue-shifted micro-jet, including the knot closest to the star. Proper motions for the innermost knots on each side are estimated to be 0. 0035 yr−1 and 0. 0047 yr−1 for the red- and blue-shifted jets, respectively. Based on this we show that new knots are ejected on an approximate timescale of 10–15 yr. Gaussian fitting to the jet axis centroids shows a point-symmetric wiggle within the inner portion of both micro-jets, indicating precession of the jet. We use the jet shape to measure a precession period of 8 yr, with a half-opening angle β < 0.6 ◦ . This precession may provide an alternative explanation for the rotation signatures previously reported. Conclusions. We find that these parameters are compatible with precession due to a brown dwarf companion orbiting at a separation of ≤0.3 au. Further observations with higher spatial resolution may help to clarify the source of this precession.