We study the correspondence between the moduli space of vacua of three-dimensional supersymmetric Yang-Mills (Maxwell) Chern-Simons theories and brane configurations with a (p,q)5-brane. For Coulomb branches, the number of the massless adjoint scalar fields in various supersymmetric theories exactly coincides with the number of the freely moving directions of D3-branes stretched between two 5-branes. When we include a matter superfield into the supersymmetric Chern-Simons theory two distinct symmetric and asymmetric phase appear. The symmetric phase is peculiar to this Chern-Simons Higgs system. We find the corresponding brane configuration for these phases. We also identify the stringy counterpart of the topological vortex state in the asymmetric phase.