In this paper, we study balanced metrics and Berezin quantization on a class of Hartogs domains defined by varOmega _n={(z_1,ldots ,z_n)in {mathbb {C}}^n:vert z_1vert<vert z_2vert<cdots<vert z_nvert <1} which generalize the so-called classical Hartogs triangle. We introduce a Kähler metric g(nu ) associated with the Kähler potential varPhi _n(z):=-sum _{k=1}^{n-1}nu _kln (vert z_{k+1}vert ^2-vert z_kvert ^2)-nu _nln (1-vert z_nvert ^2) on varOmega _n. As main contributions, on one hand we compute the explicit form for Bergman kernel of weighted Hilbert space, and then, we obtain the necessary and sufficient condition for the metric g(nu ) on the domain varOmega _n to be a balanced metric. On the other hand, by using the Calabi’s diastasis function, we prove that the Hartogs triangles admit a Berezin quantization.