We propose the results of a theoretical and mathematical model of the growing bubbles at low Mach number in a generalized Newtonian fluid. The system occurs under the effect of magnetic field and shear stress. The mathematical model is formulated and solved analytically on the basis of mass equation, Navier–Stokes equation, and diffusion equation. Analysis of the results demonstrates the role of magnetic field, shear stress, and electrical conductivity on the bubble growth process in a generalized Newtonian fluid at low Mach number; gives us the bubble radius in non-Newtonian fluid, Newtonian fluid, and viscoelastic fluid in the special cases of the flow index n; and also we get that the effect of magnetic field weakness from the behavior of gas bubble growth.