  We investigate vortices on a cylinder in supersymmetric non-Abelian gauge
theory with hypermultiplets in the fundamental representation. We identify
moduli space of periodic vortices and find that a pair of wall-like objects
appears as the vortex moduli is varied. Usual domain walls also can be obtained
from the single vortex on the cylinder by introducing a twisted boundary
condition. We can understand these phenomena as a T-duality among D-brane
configurations in type II superstring theories. Using this T-duality picture,
we find a one-to-one correspondence between the moduli space of non-Abelian
vortices and that of kinky D-brane configurations for domain walls.
