Screening various plant species to act as hyperaccumulators and associated health risks could serve as a sustainable solution for the bioremediation heavy metals (HMs). For the first time, the present study explored the phytoremediation potential of native plants, soil enrichment, and human health risks associated with the contamination of HMs in soil and plant samples collected from a municipal solid-waste open dump site. Soil and plant samples (n = 18 + 18) from the dumpsite and (n = 18) from the control site were analyzed for selected HMs, i.e., Chromium (Cr), Lead (Pb), Nickel (Ni), Iron (Fe), and Zinc (Zn). The phytoremediation potential of plants was assessed using the bioaccumulation factor (BAF), bioaccumulation coefficient (BAC), and translocation factor (TF), while soil pollution levels were evaluated using the contamination factor (CF), geoaccumulation index (Igeo), enrichment factor (EF), potential ecological risk index (PERI), and human health risk indices. The results revealed that based on TF and BAC values, Alhagi maurorum Medic., Astragalus creticus Lam., Cichorium intybus L., Berberis lycium Royle, and Datura stramonium L. were hyperaccumulators for Cr while Parthenium hysterophorus L. was a promising species for both Ni and Cr. Similarly, CF values for Fe, Ni, Pb, and Cr were >6, thereby showing very high contamination, while Igeo values for Fe, Ni, Pb, and Cr were (class 6, >5), showing that the soil was extremely polluted. Furthermore, EF values for Fe, Ni, Pb, Cr, and Zn were 2 < EF ≤ 5, depicting moderate enrichment, while PERI values were in the range of 91.31–195.84, employing moderate ecological risks (95 < PERI < 190) from the dumpsite’s soil. Moreover, for non-carcinogenic exposure, none of the analyzed metals exceeded the threshold limit HRI values > 1 in both adults and children. Likewise, in the case of carcinogenic effects, the CRI values were lower than the tolerable limits (1 × 10−6–1 × 10−4) in both adults and children. Moreover, almost all studied plants could be utilized for the phytoextraction of mentioned HMs. In future, the present study can help in the implementation of public policies to ensure sustainability and developmental activities in contaminated sites. Based on these results, it is concluded that there is a dire need of monitoring solid waste dumpsites due to various types of potential risks associated with the contamination of HMs. Moreover, to minimize the potential health problems arising from the dumpsite, it is substantive that special attention should be paid to work on sustainable and eco-friendly remedial measures.