Extrusion cooking allows the development of value-added products from pulses, such as gluten-free snacks with added functional properties. The main objective of this study was to evaluate the changes induced by the extrusion process on the carbohydrate fraction (total carbohydrates, soluble sugars and oligosaccharides, dietary fiber, and arabinoxylans) of novel flour formulations based on chickpeas and rice enriched with different dietary fiber sources. Moreover, the influence of the addition of fiber-rich ingredients, such as Fibersol^® and passion fruit, on the analyzed compounds was also evaluated. Sucrose was the main soluble sugar found in analyzed formulations, and raffinose was the prevalent oligosaccharide, followed by stachyose. The content of total α-galactosides tended to be higher after extrusion cooking. As a consequence of the extrusion treatment, the content of total and soluble dietary fiber was statistically increased in most of the analyzed samples. In general, no significant changes were observed in total arabinoxylan content as a consequence of the extrusion process, while the content of water-soluble arabinoxylans was significantly increased in extruded formulations. It was observed that the content of total available carbohydrates, stachyose, and water-soluble arabinoxylans were significantly influenced by the addition of passion fruit, Fibersol^®, and both. The incorporation of these ingredients in gluten-free formulations based on chickpeas and rice allows one to obtain suitable functional formulations for the development of innovative, gluten-free, extruded snack-type products, which could be an interesting alternative for people with celiac disease.