The generalized magneto-thermoelasticity theory, based on Green–Naghdi model, is used to study the thermal shock problem of a fiber-reinforced anisotropic half-space. The solid half-space deforms because of thermal shock, and due to the application of the magnetic field. Maxwell’s equations are formulated and the generalized coupled governing equations are derived. Finite element method with the Laplace transform technique is used to obtain the general solution. The distributions of the considered physical variables are represented graphically. The influence of the magnetic field is discussed. Some particular cases of special interest due to the application of two types of Green and Naghdi’s theory have been deduced.