By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. Display omitted •MHD flow of the generalized Maxwell fluids under AC electric field is analyzed.•The MHD flow is confined to a two-dimensional rectangular micropump.•Analytical solution is obtained by using the method of separation of variables.•The influences of related parameters on the MHD velocity are discussed.