Cadmium (Cd) contamination in soil negatively impacts crop productivity, grain quality, and human health. Wheat seeds, with different concentrations of intrinsic zinc (Zn): low Zn (35 mg kg−1), medium (42 mg kg−1), and high Zn (49 mg kg−1), were planted in artificially contaminated soil (10 mg Cd kg−1 soil). Zinc (5 g kg−1) and biochar (20 g kg−1 soil) were applied alone or in combination at sowing. Cadmium contamination reduced wheat growth, productivity, and grain Zn concentration, relative to the respective no-Cd treatments, with greater reductions in plants with low intrinsic Zn. Among the soil amendments, Zn and/or biochar improved wheat productivity and grain Zn and reduced grain Cd concentration in plants grown from seed with varying intrinsic Zn levels. Plants from high intrinsic Zn seeds performed better under Cd stress with the application of soil amendments than seeds with low or medium intrinsic Zn levels. The combined application of Zn and biochar had the highest increases in grain yield (9.51%) and grain Zn concentration (12.2%), relative to the control (no Cd, no Zn, and no biochar). This treatment also decreased the Cd concentrations in straw (7.1%) and grain (95.6%). The sole application of Zn or biochar improved wheat productivity and grain Zn concentration and deceased grain Cd concentration under Cd stress, but more improvements resulted from the combined application of Zn and biochar. Plants grown from seed with high Zn were better able to tolerate Cd stress than the plants raised from seeds with medium and low Zn levels.