  In 2+1 dimensions, we propose a renormalizable non-linear sigma model action
which describes the $\mathcal{N}=2$ supersymmetric generalization of Galilean
Electrodynamics. We first start with the simplest model obtained by null
reduction of the relativistic Abelian $\mathcal{N}=1$ supersymmetric QED in 3+1
dimensions and study its renormalization properties directly in
non-relativistic superspace. Despite the existence of a non-renormalization
theorem induced by the causal structure of the non-relativistic dynamics, we
find that the theory is non-renormalizable. Infinite dimensionless,
supersymmetric and gauge-invariant terms, which combine into an analytic
function, are generated at quantum level. Renormalizability is then restored by
generalizing the theory to a non-linear sigma model where the usual minimal
coupling between gauge and matter is complemented by infinitely many marginal
couplings driven by a dimensionless gauge scalar and its fermionic
superpartner. Superconformal invariance is preserved in correspondence of a
non-trivial conformal manifold of fixed points where the theory is
gauge-invariant and interacting.
