The surge in food delivery systems during the coronavirus 2019 pandemic necessitated this study of heavy metal migration from food contact materials (FCMs). A total of 104 samples of FCMs, comprising 51 polypropylene (PP), 21 polyethylene (PE), and 32 polystyrene (PS) samples of six different types of FCMs (containers, covers, table utensils, cups, pouches, and wrappers) used for food delivery distributed in Korea, were collected and investigated for migration of three heavy metals (Pb, Cd, and As) using inductively coupled plasma–mass spectrometry (ICP-MS) to determine whether they complied with Korea’s Standards and Specifications for Utensils, Containers, and Packages. Acetic acid (4%, v/v) was used as the food simulant, and tests were performed at 100oC (in harsh conditions) for 30 min. Linearity of Pb, Cd, and As showed acceptable results with a coefficient of determination (R2) value of 0.9999. Limit of detection (LOD) and limit of quantification (LOQ) of Pb, Cd, and As were 0.001, 0.001, and 0.001 μg/L and 0.002, 0.003, and 0.003 μg/L, respectively. Accuracy and precision results complied with the criteria presented in the European Commission Joint Research Centre guidelines. The average concentration of Pb, Cd, and As migration detected in a total of 104 samples was 0.009–0.260 μg/L, which was very low compared with the migration specification set in the Standards and Specifications for Utensils, Containers, and Packages. The maximum level of Pb corresponded to 0.23% of the migration limit. There were no samples exceeding the limit. Thus, this study confirmed that the heavy metal contents of FCMs used for delivery food distributed in Korea were safely managed. The data from this study represent an invaluable source for science-based safety management of hazardous heavy metals migrating from FCMs used in the food delivery industry.