A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with $N=1$ supersymmetry. Extensive use is made of the superfield supercurrent that places the supercurrent ${J}_{\ensuremath{\alpha}}^{\ensuremath{\mu}},$ energy-momentum tensor ${\ensuremath{\Theta}}^{\ensuremath{\mu}\ensuremath{\nu}},$ and topological current ${\ensuremath{\zeta}}^{\ensuremath{\mu}}$ in a supermultiplet to study the structure of supersymmetry and related superconformal symmetry in the presence of solitons. It is shown that the supermultiplet structure of ${(J}_{\ensuremath{\alpha}}^{\ensuremath{\mu}},{\ensuremath{\Theta}}^{\ensuremath{\mu}\ensuremath{\nu}},{\ensuremath{\zeta}}^{\ensuremath{\mu}})$ is kept exact while the topological current ${\ensuremath{\zeta}}^{\ensuremath{\mu}}$ acquires a quantum modification through the superconformal anomaly. In addition, the one-loop superfield effective action is explicitly constructed to verify the BPS saturation of the soliton spectrum as well as the effect of the anomaly.