We present a comprehensive data set of supernova (SN) 2016adj located within the central dust lane of Centaurus A. SN 2016adj is significantly reddened and after correcting the peak apparent B-band magnitude (m_B = 17.48 ± 0.05) for Milky Way reddening and our inferred host-galaxy reddening parameters (i.e., R_V^host = 5.7±0.7 and A_V^host = 6.3 ± 0.2 mag), we estimated it reached a peak absolute magnitude of M_B ∼ −18. A detailed inspection of the optical and near-infrared (NIR) spectroscopic time series reveals a carbon-rich SN Ic and not a SN Ib/IIb as previously suggested in the literature. The NIR spectra show prevalent carbon-monoxide formation occurring already by +41 days past B-band maximum, which is ≈11 days earlier than previously reported in the literature for this object. Interestingly, around two months past maximum, the NIR spectrum of SN 2016adj begins to exhibit H features, with a +97 days medium resolution spectrum revealing both Paschen and Bracket lines with absorption minima of ∼2000 km s⁻¹, full-width-half-maximum emission velocities of ∼1000 km s⁻¹, and emission line ratios consistent with a dense emission region. We speculate that these attributes are due to a circumstellar interaction (CSI) between the rapidly expanding SN ejecta and a H-rich shell of material that formed during the pre-SN phase. A bolometric light curve was constructed and a semi-analytical model fit suggests the SN synthesized 0.5 M_⊙ of ⁵⁶Ni and ejected 4.7 M_⊙ of material, though these values should be approached with caution given the large uncertainties associated with the adopted reddening parameters and known light echo emission. Finally, inspection of the Hubble Space Telescope archival data yielded no progenitor detection.