Bone problems in the population begin to be establish in childhood. The present study aims to assess the usual calcium, phosphorus, magnesium, and vitamin D intakes, along with the food sources of these nutrients, in Spanish children participating in the EsNuPI (Estudio Nutricional en Población Infantil Española) study. Two 24 h dietary recalls were applied to 1448 children (1 to <10 years) divided into two sub-samples: one reference sample (RS) of the general population [n = 707] and another sample which exclusively included children consuming enriched or fortified milks, here called “adapted milks” (AMS) [n = 741]. Estimation of the usual intake shows that nutrient intake increased with age for all nutrients except vitamin D. Using as reference the Dietary Reference Values from the European Food Safety Authority (EFSA), calcium and magnesium intakes were found to be below the average requirement (AR) and adequate intake (AI), respectively, in a considerable percentage of children. Furthermore, phosphorus exceeded the AI in 100% of individuals and vitamin D was lower than the AI in almost all children studied. The results were very similar when considering only plausible reporters. When analyzing the food sources of the nutrients studied, milk and dairy products contributed the most to calcium, phosphorus, magnesium, and vitamin D. Other sources of calcium were cereals and vegetables; for phosphorus: meat, meat products, and cereals; for magnesium: cereals and fruits; and, for vitamin D: fish and eggs. These results highlight the desirability of improving the intake concerning these nutrients, which are involved in bone and metabolic health in children. The AMS group appeared to contribute better to the adequacy of those nutrients than the RS group, but both still need further improvement. Of special interest are the results of vitamin D intakes, which were significantly higher in the AMS group (although still below the AI), independent of age.