Basalt fiber (BF) has received much attention in recent years for engineering practice and scientific research related to basalt fiber reinforced concrete (BFRC) due to its advantageous mechanical properties and cost-effectiveness. By researching its performance characteristics after cryogenic freeze–thaw cycles, the advantages of BFRC’s mechanical properties can be further exploited in order to expand its application scope. The effects of the fiber volume fraction, temperature gradient, and number of freeze–thaw cycles on the compressive strength, toughness index, splitting tensile strength, flexural strength, etc., of BFRC were investigated. Additionally, the damage mechanism of BFRC after freeze–thaw cycles was analyzed via scanning electron microscopy (SEM). The results show that the compressive strength of BFRC reaches its peak value when the fraction reaches 0.1% under the conditions of freezing and thawing cycles from room temperature to −80 °C. When the fraction of BFRC is 0.1%, and the maximum reduction is 17.1%, the splitting tensile strength decreased most sharply when the fraction was 0.1%, and the decrease amplitude was 40.9%, and the flexural strength decreased most acutely when the fraction was 0.3%, and the maximum decrease was 44.62%. The addition of basalt fibers can reduce the damage to the microstructure of concrete and improve its plastic degradation characteristics to a certain extent. With a decrease in the minimum temperature of the cryogenic freeze–thaw cycle, the optimal fiber content for compressive strength increases. Nevertheless, the splitting tensile strength and flexural strength of BFRC is improved as the fiber content increases under the cryogenic freeze–thaw environment.