Geopolymer composites have been around only for 40 years. Nowadays, they are used in buildings and infrastructures of various kinds. A geopolymer’s main benefit is that it is a green material that is partially made by utilizing waste products. The carbon footprint from geopolymer matrix manufacturing is at least two times less than Portland cement manufacturing. Due to the nature of the geopolymer manufacturing process, there is a high risk of shrinkage that could develop unwanted micro-cracks that could reduce strength and create higher creep strains. Because of this concern, a common strategy to reduce long-term strains of the material, such as shrinkage and creep, is to add fiber reinforcement that would constrain crack development in the material. This article aims to determine how various kinds and amounts of different fiber reinforcement affect fly ash-based geopolymer composites’ creep strains in compression. Specimen mixes were produced with 1% steel fibers, 1% polypropylene fibers, 5% polypropylene fibers, and without fibers (plain geopolymer). For creep and shrinkage testing, cylindrical specimens Ø46 × 190 mm were used. The highest creep resistance was observed in 5% polypropylene fiber specimens, followed by 1% polypropylene fiber, plain, and 1% steel fiber specimens. The highest compressive strength was observed in 1% polypropylene fiber specimens, followed by plain specimens, 1% steel fiber specimens, and 5% polypropylene fiber-reinforced specimens. The only fiber-reinforced geopolymer mix with improved long-term properties was observed with 1% polypropylene fiber inclusion, whereas other fiber-introduced mixes showed significant decreases in long-term properties. The geopolymer composite mix with 1% polypropylene fiber reinforcement showed a reduction in creep strains of 31% compared to the plain geopolymer composite.