High-pressure homogenization (HPH) is an emerging technology for obtaining physical and microbial stability of plant-based milks, but there is little information on the effects of this technology on the phytochemical components of the processed plant food beverage and during its cold storage. The effect of three selected HPH treatments (180 MPa/25 °C, 150 MPa/55 °C, and 50 MPa/75 °C) and pasteurization (PAS) (63 °C, 20 min) on minor lipid constituents, total proteins, phenolic compounds, antioxidant capacity, and essential minerals of Brazil nut beverage (BNB) were studied. Additionally, the study of the possible changes in these constituents was carried out during cold storage at 5 °C for 21 days. The fatty acid profile (dominated by oleic acid and linoleic acid), free fatty acid content, protein, and essential minerals (notable source of Se and Cu) of the processed BNB remained almost stable to treatments (HPH and PAS). Specifically, reductions in squalene (22.7 to 26.4%) and γ-γ-tocopherol (28.4 to 36%) were observed in beverages processed via both non-thermal HPH and thermal PAS, but β-sitosterol remained unchanged. Total phenolics were reduced (24 to 30%) after both treatments, a factor that influenced the observed antioxidant capacity. The studied individual phenolics in BNB were gallic acid, catechin, epicatechin, catechin gallate, and ellagic acid, being the most abundant compounds. During cold storage (5 °C) up to 21 days, changes in the content of phytochemicals, minerals, and total proteins were not noticeable for any treated beverages, and no lipolysis processes were promoted. Therefore, after the application of HPH processing, Brazil nut beverage (BNB) maintained almost unaltered levels of bioactive compounds, essential minerals, total protein, and oxidative stability, remarkable characteristics for its potential development as a functional food.