Constructed wetlands (CWs) are important plant filters used for wastewater treatment. The behavior of the Canna indica-planted CWs in the face of a highly variable composition of industrial wastewater has yet to be understood. Here, we show the effectiveness of Canna indica-planted and unplanted vertical subsurface flow CWs for the treatment of Algiers petroleum refinery’s effluent. The selected species was placed in the CWs containing light expanded clay aggregate (LECA) and sand as a substrate. The findings indicate that the planted constructed wetlands efficiently removed 85% of total suspended solids (TSS), 96.38% of total nitrogen (TN), 96.15% of nitrate nitrogen (NO3−-N), 99.15% of ammonium nitrogen (NH4+-N), and 99.87% of nitrite nitrogen (NO2−-N). The overall mean removal efficiencies for heavy metals in the vegetated CWs were considerably greater than those of the control. Concentrations of Cr, Cu, Fe, Pb, Zn, Al, Ni, and Cd were calculated in the roots, rhizomes, leaves, and stems of the plant; then, the bioaccumulation factor (BAF) and translocation factor (TF) were determined. An initial examination using scanning electron microscopy (SEM–EDX) was also included in the study. The analysis indicated that toxic elements were adsorbed on plant tissues, concentrated in the roots, and partially transported to the aerial parts. These results are useful for the design of CWs to treat industrial wastewater, enabling water of acceptable quality to be discharged into the environment, especially as a low maintenance and cost-effective technology in developing countries.