The aim of this paper is to analyze the influence of hybrid fiber reinforcement on the properties of a lightweight fly ash-based geopolymer. The matrix includes the ratio of fly ash and microspheres at 1:1. Carbon and steel fibers have been chosen due to their high mechanical properties as reinforcement. Short steel fibers (SFs) and/or carbon fibers (CFs) were used as reinforcement in the following proportions: 2.0% wt. CFs, 1.5% wt. CFs and 0.5% wt. SFs, 1.0% wt. CFs and 1.0% wt. SFs, 0.5% wt. CFs and 1.5% wt. SFs and 2.0% wt. SFs. Hybrid reinforcement of geopolymer composites was used to obtain optimal strength properties, i.e., compressive strength due to steel fiber and bending strength due to carbon fibers. Additionally, reference samples consisting of the geopolymer matrix material itself. After the production of geopolymer composites, their density was examined, and the structure (using scanning electron microscopy) and mechanical properties (i.e., bending and compressive strength) in relation to the type and amount of reinforcement. In addition, to determine the thermal insulation properties of the geopolymer matrix, its thermal conductivity coefficient was determined. The results show that the addition of fiber improved compressive and bending strength. The best compressive strength is obtained for a steel fiber-reinforced composite (2.0% wt.). The best bending strength is obtained for the hybrid reinforced composite: 1.5% wt. CFs and 0.5% wt. SFs. The geopolymer composite is characterized by low thermal conductivity (0.18–0.22 W/m ∙ K) at low density (0.89–0.93 g/cm3).