  Let $\mathcal{H}$ be a separable Hilbert space and let
$A^{2}_{\varphi}(\mathcal{H})$ be the $\mathcal{H}$-valued Bergman spaces with
exponential weights. In the present paper, we give the complete
characterizations for the boundedness and compactness of Hankel operators on
$A^{2}_{\varphi}(\mathcal{H})$. For $p\geq2$, the Schatten $p$-classes of the
Hankel operator with conjugate analytic symbols are studied.
