  Recently, a non-relativistic off-shell formulation of three dimensional
Newton-Cartan supergravity was proposed as the $c \rightarrow \infty$ limit of
three dimensional $\mathcal{N}=2$ supergravity in arXiv:1505.02095. In the
present paper we study supersymmetric backgrounds within this theory. Using
integrability constraints for the non-relativistic Killing spinor equations, we
explicitly construct all maximally supersymmetric solutions, which admit four
supercharges. In addition to these solutions, there are $\frac{1}{2}$-BPS
solutions with reduced supersymmetry. We give explicit examples of such
backgrounds and derive necessary conditions for backgrounds preserving two
supercharges. Finally, we address how supersymmetric backgrounds of
$\mathcal{N}=2$ supergravity are connected to the solutions found here in the
$c \rightarrow \infty$ limit.
