The design of transparent optical materials with stimulated Brillouin scattering (SBS) suppression is a topic of current interest. We measured two-photon absorption (2PA) cross-section σ2PA and Brillouin gain factor gB of a suspension of hexagonal boron nitride (hBN) in N-methyl-2-pyrrolidone at the second harmonic of a Nd:YAG laser. SBS exhibits a significant quenching with hBN concentration, like previously observed in graphene suspension. The melting of hBN flakes due to a large 2PA and the related changes in the acoustic damping coefficient explain the quenching mechanism.