We propose a monolithic mode separator (MS) for the first-order spatial mode of a light field. The principle of the MS is an asymmetric Mach-Zehnder interferometer, which consists of two non-polarizing beam splitters, a right-angle prism, and a pentagonal prism. These optics are glued together as a monolithic one. The phase difference between the two light paths inside the interferometer is temperature controlled. The separation efficiency for two first-order orthogonal Hermite Gaussian (HG) modes, i.e., HG01 and HG10, is 97.5%, and the overall transmission is 77%. The device is intrinsically stable and convenient to be adopted in various experiments.