We investigate a strain-induced topological phase transition in the ferromagnetic Janus monolayer MnSbBiS2Te2 using first-principles calculations. The electronic, magnetic, and topological properties are studied under biaxial strain within the range of -8 to +8%. The ground state of monolayer MnSbBiS2Te2 is metallic with an out-of-plane magnetic easy axis. A band gap is opened when a compressive strain between -4% and -7% is applied. We observe a topological phase transition at a biaxial strain of -5%, where the material becomes a Chern insulator exhibiting a quantum anomalous hall (QAH) effect. We find that biaxial strain and spin-orbit coupling (SOC) are responsible for the topological phase transition in MnSbBiS2Te2. In addition, we find that biaxial strain can alter the direction of the magnetic easy axis of MnSbBiS2Te2. The Curie temperature is calculated using the Heisenberg model and is found to be 24 K. This study could pave the way to the design of topological materials with potential applications in spintronics, quantum computing, and dissipationless electronics.