This study investigated the effect of crude protein (CP) and non-essential amino acid (NEAA) supplementation on the growth performance, blood profile, intestinal morphology, mRNA relative abundance of inflammatory and antioxidant markers, and tight junction proteins in piglets over the first 2 weeks after weaning. Ninety 21-day-old piglets (7.55 ± 0.72 kg) were assigned in a randomized block design to one of three dietary treatments: (1) high CP, a diet with 24% CP; (2) low CP, a diet with 18% CP; and (3) low CP + NEAA, a diet with 18% CP supplemented with 5 g/kg Arg (L-arginine; purity >99%) and 10 g/kg Glu + Gln (minimum 10% L-glutamine and minimum 10% L-glutamate). Piglets were fed with corn-soybean meal basal diets in a 14-day trial. There was an improvement (p < 0.05) in the feed conversion ratio of piglets fed the high-CP diet compared to treatments with low CP or low CP + NEAA. Serum urea nitrogen was higher (p < 0.05) in piglets fed high CP compared to other dietary treatments. In the duodenum, the villus height of animals fed the low-CP + NEAA diets was greater (p < 0.05) than those fed with the high- and low-CP diets. The goblet cell proportion of piglets fed low CP + NEAA or high CP was higher (p < 0.05) compared to low CP. In the jejunum, the crypt depth of the piglets with the high-CP dietary treatment was greater (p < 0.05) in comparison with low CP + NEAA. In the jejunum, IFN-γ mRNA expression was higher (p < 0.05) in animals fed the high-CP diets compared to other dietary treatments. However, superoxide dismutase and occludin mRNA expression were higher (p < 0.05) in animals fed low CP + NEAA than in piglets on the high-CP diets. In the ileum, the number of Peyer’s patches in piglets fed high CP was higher (p < 0.05) compared to other dietary treatments. In conclusion, the high-CP diet (24% CP) improves the feed conversion of piglets in the first 2 weeks after weaning compared to the low-CP diet (18% CP) supplemented or not with NEAA. However, the low-CP diet supplemented with NEAA (Arg, Gln, and Glu) improves intestinal health in piglets by promoting greater villus height and proportion of goblet cells in the duodenum, reducing jejunal crypt depth, and reducing Peyer’s number patches in the ileum. In addition, piglets that received the low-CP + NEAA diet showed an increase in superoxide dismutase and occludin and a lower expression of IFN-γ mRNA.