Aims. Stripped envelope (SE) supernovae are explosions of stars that have somehow lost most of their outer envelopes. We present the discovery and analyse the observations of the Type Ib supernova 2019odp (a.k.a. ZTF19abqwtfu) covering epochs within days of the explosion to late nebular phases at 360 d post-explosion.Methods. Our observations include an extensive set of photometric observations and low- to medium-resolution spectroscopic observations, both covering the complete observable time range. We analysed the data using analytic models for the recombination cooling emission of the early excess emission and the diffusion of the peak light curve. We expanded on existing methods to derive oxygen mass estimates from nebular phase spectroscopy, and briefly discuss progenitor models based on this analysis.Results. Our spectroscopic observations confirm the presence of He in the supernova ejecta and we thus (re)classify SN 2019odp as a Type Ib supernova. From the pseudo-bolometric light curve, we estimate a high ejecta mass of Mej ∼ 4 − 7 M⊙. The high ejecta mass, large nebular [O I]/[Ca II] line flux ratio (1.2 − 1.9), and an oxygen mass above ⪆0.5 M⊙ point towards a progenitor with a pre-explosion mass higher than 18 M⊙. Whereas a majority of analysed SE supernovae in the literature seem to have low ejecta masses, indicating stripping in a binary star system, SN 2019odp instead has parameters that are consistent with an origin in a single massive star. The compact nature of the progenitor (≲10 R⊙) suggests that a Wolf-Rayet star is the progenitor.