The stress field of a functionally graded material rotating disk is studied for different cases of non-uniform thickness variation in the magneto-thermal environment. Three different cases of thickness variation are considered by assuming the variation of non-uniform thickness profiles to be linear, rational, and exponential functions of radius. The mass of the functionally graded material disk is considered equal in all cases of uniform/non-uniform thickness variation. The finite-difference method is used to obtain the numerical results for an Al/Al2O3 functionally graded material disk of fixed-free boundary conditions. The resultant thermo-elastic analysis has shown that the decrease in outer end thickness significantly increases circumferential stress at that end. In the absence of a magnetic field, for the disk with thin outer end thickness minimum stress intensity can be found with linearly varying thickness profile, and high intensity of circumferential stress in case rational and exponential variation of thickness profiles can significantly be reduced with an optimum magnetic field. The transient stress fields and the effect of material properties are also analyzed in detail. All the analyses showed that along with affecting the magnitude, the presence of the magnetic field changes the location and nature of maximum stress in the disk. Finally, results are compared with the finite-element method and available analytical results to verify the analysis.