We propose a connection-based characterization for multiplicative intuitionistic linear logic ({\MILL}) which is based on labels and constraints that capture Urquhart's possible world semantics of the logic. We first briefly recall the purely syntactic sequent calculus for {\MILL}, which we call LMILL. Then, in the spirit of our previous results on the Logic of Bunched Implications (BI), we present a connection-based characterization of MILL provability. We show its soundness and completeness without the need for any notion of multiplicity. From the characterization, we finally propose a labelled sequent calculus for MILL.