  In this work we investigate properties of a supersymmetric extension of the
quantum spherical model from an off-shell formulation directly in the
superspace. This is convenient to safely handle the constraint structure of the
model in a way compatible with supersymmetry. The model is parametrized by an
interaction energy, $U_{{\bf r},{\bf r}'}$, which governs the interactions
between the superfields of different sites. We briefly discuss some
consequences when $U_{{\bf r},{\bf r}'}$ corresponds to the case of
first-neighbor interactions. After computing the partition function via saddle
point method for a generic interaction, $U_{{\bf r},{\bf r}'}\equiv U(|{\bf
r}-{\bf r}'|)$, we focus in the mean-field version, which reveals an
interesting critical behavior. In fact, the mean-field supersymmetric model
exhibits a quantum phase transition without breaking supersymmetry at zero
temperature, as well as a phase transition at finite temperature with broken
supersymmetry. We compute critical exponents of the usual magnetization and
susceptibility in both cases of zero and finite temperature. Concerning the
susceptibility, there are two regimes in the case of finite temperature
characterized by distinct critical exponents. The entropy is well behaved at
low temperature, vanishing as $T \rightarrow 0$
