  We consider renormalization of the central charge and the mass of the ${\cal
N}=2$ supersymmetric Abelian vortices in 2+1 dimensions. We obtain ${\cal N}=2$
supersymmetric theory in 2+1 dimensions by dimensionally reducing the ${\cal
N}=1$ SQED in 3+1 dimensions with two chiral fields carrying opposite charges.
Then we introduce a mass for one of the matter multiplets without breaking N=2
supersymmetry. This massive multiplet is viewed as a regulator in the large
mass limit. We show that the mass and the central charge of the vortex get the
same nonvanishing quantum corrections, which preserves BPS saturation at the
quantum level. Comparison with the operator form of the central extension
exhibits fractionalization of a global U(1) charge; it becomes 1/2 for the
minimal vortex. The very fact of the mass and charge renormalization is due to
a "reflection" of an unbalanced number of the fermion and boson zero modes on
the vortex in the regulator sector.
