Dietary uptake of heavy metals through the consumption of vegetables grown on polluted soil can have serious human health implications. Thus, the study presented in this paper investigated the bioaccumulation and associated dietary risks of Pb, Zn, and Cd present in vegetables widely consumed in Nigeria, namely amaranth and jute mallow, grown on soil irrigated with polluted water from Asa River. The study found that the soil was polluted with Zn, Pb, and Cd with Pb and Cd being contributed by polluted river, while Zn was from geogenic sources. The metal concentration in amaranth and jute mallow varied in the order of Zn > Pb > Cd and Zn > Pb ≈ Cd, respectively. Jute mallow acts as an excluder plant for Pb, Cd, and Zn. Consequently, the metal concentrations in jute mallow were below the toxic threshold levels. Furthermore, non-cancer human health risk of consuming jute mallow from the study site was not significant. In contrast, the concentrations of Pb and Cd in amaranth were found to be above the recommended safe levels and to be posing human health risks. Therefore, further investigation was undertaken to identify the pathways of heavy metals to amaranth. The study found that the primary uptake pathway of Pb and Cd by amaranth is foliar route, while root uptake is the predominant pathway of Zn in amaranth.