Potentially toxic elements (PTEs), such as Cu, Zn, Pb, Ni, Cr, and Co, can accumulate in vineyard soils due to repeated uses of inorganic pesticides and chemical or organic fertilizers. In sloping vineyards, PTEs can also be moved by soil erosion resulting in their accumulation in low-energy zones within the landscape, adversely affecting the soil environment. Our study evaluated the ecological risk related to the pseudo-total and bioavailable PTE contents (Zn, Pb, Co, Ni, Cr, and Cu) in the soil and eroded sediment samples from an organic vineyard in Tokaj (NE Hungary). The contamination status and the ecological risk of target PTEs were assessed by calculating the contamination factor, the pollution load index, the ecological risk factor, and the ecological risk index. The median pollution load indices of 1.15, 1.81, and 1.10 for the topsoil, the sediments, and the subsoil, respectively, demonstrate a moderate multi-element contamination case in the organic vineyard. Target PTEs tented to show increased concentrations in eroded sediments with the highest enrichment ratio (3.36) observed for Cu (Cu in the sediment/Cu in the topsoil), revealing a preferential movement of Cu-rich soil particles by overland flow. Moreover, PTEs were present in the sediments in more bioavailable forms (except Ni, Cr), assessed by an extraction procedure with EDTA. The ecological risk index (< 90) based on the studied PTEs showed an overall low ecological risk in the vineyard. Copper was the predominant factor of the ecological risk. Moreover, the highest ecological risk factor (24.6) observed for the bioavailable Cu content in an eroded sediment sample (representing 82% of the total ecological risk) shows that Cu accumulation in sloping vineyards is an ecological risk, particularly in the sedimentation zones. The high proportions of bioavailable Cu in the vineyard’s soil represent an increasing ecological risk over time, related to repeated treatments of vine plants with Cu-based pesticides.