  Let $\mathbf{k}$ be a field of arbitrary characteristic, let $\Lambda$ be a
finite dimensional $\mathbf{k}$-algebra, and let $V$ be a finitely generated
$\Lambda$-module. F. M. Bleher and the third author previously proved that $V$
has a well-defined versal deformation ring $R(\Lambda,V)$. If the stable
endomorphism ring of $V$ is isomorphic to $\mathbf{k}$, they also proved under
the additional assumption that $\Lambda$ is self-injective that $R(\Lambda,V)$
is universal. In this paper, we prove instead that if $\Lambda$ is arbitrary
but $V$ is Gorenstein-projective then $R(\Lambda,V)$ is also universal when the
stable endomorphism ring of $V$ is isomorphic to $\mathbf{k}$. Moreover, we
show that singular equivalences of Morita type (as introduced by X. W. Chen and
L. G. Sun) preserve the isomorphism classes of versal deformation rings of
finitely generated Gorenstein-projective modules over Gorenstein algebras. We
also provide examples. In particular, if $\Lambda$ is a monomial algebra in
which there is no overlap (as introduced by X. W. Chen, D. Shen and G. Zhou) we
prove that every finitely generated indecomposable Gorenstein-projective
$\Lambda$-module has a universal deformation ring that is isomorphic to either
$\mathbf{k}$ or to $\mathbf{k}[\![t]\!]/(t^2)$.
