This paper presents the results of research on geopolymer composites based on fly ash with the addition of melamine fibers in amounts of 0.5%, 1% and 2% by weight and, for comparison, without the addition of fibers. The melamine fibers used in the tests retain their melamine resin properties by 100% and are characterized by excellent acoustic and thermal insulation as well as excellent filtration. In addition, these fibers are nonflammable, resistant to chemicals, resistant to UV radiation, characterized by high temperature resistance and, most importantly, do not show thermal-related shrinking, melting and dripping. This paper presents the results of density measurements, compressive and flexural strength as well as the results of the measurement of thermal radiation changes in samples subjected to a temperature of 600 °C. The results indicate that melamine fibers can be used as geopolymer reinforcement. The best result was achieved for 0.5% by weight amount of reinforcement, approximately 53 MPa, compared to 41 MPa for a pure matrix. In the case of flexural strength, the best results were obtained for the samples made of unreinforced geopolymer and samples with the addition of 0.5% by weight of melamine fibers, which were characterized by bending strength values above 9 MPa, amounting to 10.7 MPa and 9.3 MPa, respectively. The thermal radiation measurements and fire-jet test did not confirm the increasing thermal and fire resistance of the composites reinforced by melamine fiber.