Toxic elements have a negative impact on health, especially among infants and young children. Even low levels of exposure can impair the normal growth and development of children. In young children, all organs and metabolic processes are insufficiently developed, making them particularly vulnerable to the effects of toxic elements. The aim of this study is to estimate the concentration of toxic elements in products consumed by infants and young children. The health risk of young children due to consumption of ready-made products potentially contaminated with As (arsenic), Cd (cadmium), Hg (mercury), and Pb (lead) was also assessed. A total of 397 samples (dinners, porridges, mousses, snacks “for the handle”, baby drinks, dairy) were analyzed for the content of toxic elements. Inductively coupled plasma mass spectrometry (ICP-MS) was used to assess As, Cd, and Pb concentration. The determination of Hg was performed by atomic absorption spectrometry (AAS). In order to estimate children’s exposure to toxic elements, the content of indicators was also assessed: estimated daily intake (EDI), estimated weekly intake (EWI), provisional tolerable weekly intake (PTWI), provisional tolerable monthly intake (PTMI), the benchmark dose lower confidence limit (BMDL), target hazard quotient (THQ), hazard index (HI), and cancer risk (CR). The average content of As, Cd, Hg, and Pb for all ready-made products for children is: 1.411 ± 0.248 µg/kg, 2.077 ± 0.154 µg/kg, 3.161 ± 0.159 µg/kg, and 9.265 ± 0.443 µg/kg, respectively. The highest content As was found in wafer/crisps (84.71 µg/kg); in the case of Cd, dinners with fish (20.15 µg/kg); for Hg, dinners with poultry (37.25 µg/kg); and for Pb, fruit mousse (138.99 µg/kg). The results showed that 4.53% of the samples attempted to exceed Pb, and 1.5% exceeded levels of Hg. The highest value of THQ was made in the case of drinks, for Cd and Pb in mousses for children, and Hg for dairy products. The THQ, BMDL, and PTWI ratios were not exceeded. The analyzed ready-to-eat products for children aged 0.5–3 years may contain toxic elements, but most of them appear to be harmless to health.