Three-dimensional modulated electrostatic ion-acoustic wave packet in magnetized plasma with electrons obeying kappa distribution is investigated. The standard reductive perturbation theory is used to derive the corresponding three-dimensional nonlinear Schrödinger (3D-NLS) equation which governs the dynamics, as well as the slow modulation of the ion-acoustic wave packets. Both the dispersive and the nonlinear coefficients of the 3D-NLS equation are modified by the inclusion of the transverse velocity perturbations, as well as the external magnetic field. New instability regimes arise when the ion to electron temperature ratio σi, the spectral index κ (i.e. measuring deviation from Maxwellian equilibrium), and the ion gyrofrequency ωci are presented. Importantly, the latter establishes new instability regimes that are not presented in an unmagnetized plasma.