Celiac disease (CD) is a chronic disease caused by the consumption of gluten foods and is closely related to type 1 diabetes (T1D). Adherence to a gluten-free (GF) diet is the cornerstone of treating CD, and certain plant proteins added to GF foods affect blood glucose to varying degrees. The aim of this study was to analyze and compare the changes in glycemic index (GI) and incremental area under the postprandial glucose tolerance curve (IAUC) of various foods through consumption of GF foods supplemented with certain plant proteins in non-human primates. The test foods were GF rice cakes with 5%, 10%, and 15% added single plant proteins (rice protein, soy protein, and pea protein) mixed with rice flour, as well as 5%, 10%, and 15% gluten rice cakes, and rice flour alone, for a total of 13 food items, and 12 healthy cynomolgus monkeys were examined for their glucose levels in the blood after fasting and after eating each test food (50 g) for 15, 30, 45, 60, 90, and 120 min after fasting and eating each test food. Fingertip blood glucose levels were measured, and the nutrient content of each food, including protein, fat, starch, ash, and amino acids, was examined. All foods tested had a low GI (<50) when analyzed using one-way ANOVA and nonparametric tests. Postprandial IAUC was significantly lower (p < 0.05) for GF rice cakes with 15% pea protein (499.81 ± 34.46) compared to GF rice cakes with 5% pea protein (542.19 ± 38.78), 15% soy protein (572.94 ± 72.74), and 15% rice protein (530.50 ± 14.65), and GF rice cakes with 15% wheat bran protein (533.19 ± 34.89). A multiple regression analysis showed that glycine was negatively associated with IAUC in GF rice cakes with 5%, 10%, and 15% pea protein added (p = 0.0031 < 0.01). Fat was negatively correlated with IAUC in GF rice cakes supplemented with 5%, 10%, and 15% soy protein (p = 0.0024 < 0.01). In this study, GF rice cakes made with added pea protein were superior to other gluten and GF rice cakes and had a small effect on postprandial glucose.