In the present study, basalt fiber was used to enhance the low-temperature performance of asphalt mixtures in heavily frozen areas. By conducting three-point bending tests at various temperatures (−10 °C, −20 °C and −30 °C) and basalt fiber contents (0.2–0.5%), the changing trends of the bending stress, bending strain, and strain energy density were investigated and discussed. The fracture type of each asphalt mixture was distinguished based on the bending coefficient, and the micromorphology and microstructures of each basalt fiber-reinforced asphalt mixture were observed via scanning electron microscopy. The results show that basalt fiber effectively improves the low-temperature performance of an asphalt mixture and enhances its adaptability to a lower-temperature environment. The optimum fiber content of an AC-13 asphalt mixture is 0.4% based on its low-temperature performance, whereas that of an AC-20 mixture is 0.3%. Under the optimum fiber content, the low-temperature failure type of an asphalt mixture changes from brittle failure to flexible failure at −20 °C. The basalt fiber network enhances the integrity of the asphalt mixture and delays the extension of microcracks.