(1) Background: This study investigated the effect of the lactation period and the type of infant formula on the content of amino acids and selected minerals in an infant's food; (2) Methods: The study material consisted of breast milk (colostrum, n = 38; transitional milk, mature milk, n = 38) and three types of infant formulas (for first and follow-on feeding). Amino acid content was determined using an automatic amino acid analyzer, while minerals were determined by the atomic absorption spectrometry (AAS) technique; (3) Results: Breast milk and infant formulas contained a full range of essential amino acids. In most cases, the content of individual amino acids and minerals decreased with increasing lactation. In infant formulas, there were higher contents of phenylalanine, glutamic acid, proline, serine, and tyrosine in follow-on milk (p < 0.05). The EAA/TAA ratio in breast milk and infant formulas was similar, but the milk differed in their qualitative composition. Infant formulas contained levels of individual minerals that were several times higher-especially Mg, Ca, Mn, and Fe.; (4) Conclusions: Colostrum is more concentrated, and the level of amino acids and minerals is higher in it; as the milk matures, it decreases. In most cases, the content of individual amino acids and minerals is higher in infant formulas than in human milk, which is established through strict Codex Alimentarius procedures to ensure the proper development of infants.