The aim of the research was to determine the impact of potato cultivation management and weeding systems on weed infestation and to evaluate the possibility of using biomarkers to assess consumer exposure to herbicide residues in potato tubers. The experiment was carried out in 2016–2018 in Central-Eastern Poland. The subject of research was the very early variety Lord. The experiment was established using the randomized block method in a split-plot design. The first order factor was cultivation management: (A) traditional and (B) under polyethylene sheeting (PE-sheeting) put “on flat”. The second-order factors were weed control systems: (a) mechanical (b) to (d)-chemical. The study determined the degree of damage to crops and weeds, fresh and dry weight of weeds, their number and floristic composition, and herbicide residues in tubers and in the soil. The fresh and dry mass of weeds was most effectively limited by mechanical and chemical treatment with the use of a preparation containing linuron. Managing potato cultivation with PE-sheeting and soil herbicides has proven to be safe for very early potato production. Used for pre-emergence care, the preparation containing linuron did not leave even trace amounts of this active substance in the tubers. The determined amount of the active substance fluorochloridon and clomazone was lower than the Maximum Residue Level (MRL) norm in the EU (European Union). As a result, the adopted, innovative management and weeding control systems in the cultivation of early potato varieties can be considered safe for the consumer.