This paper presents a Markov-based system model for microfluidic molecular communication (MC) channels. By discretizing the advection-diffusion dynamics, the proposed model establishes a physically consistent state-space formulation. The transition matrix explicitly captures diffusion, advective flow, reversible binding, and flow-out effects. The resulting discrete-time formulation enables analytical characterization of both transient and equilibrium responses through a linear system representation. Numerical results verify that the proposed framework accurately reproduces channel behaviors across a wide range of flow conditions, providing a tractable basis for the design and analysis of MC systems in microfluidic environments.