The present paper investigates the static and dynamic polarizabilities of a two-dimensional D − ion under the influence of a magnetic field. The three-body system's Schrödinger equation is solved using a precise ab initio approach, correlating the spherical radial coordinates by means of hyperspherical coordinates. The spectrum is obtained using Born-Oppenheimer-like potential curves, in which the magnetic field is accounted for as a harmonic potential term. The polarizability is determined by employing a fast convergent variationally stable treatment.