We present, in the N = 2, D = 4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N = 2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N = 2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N = 2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U(1)-factor in the N = 2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic [Bcorrections arise at leading order. These holomorphic contribution are consistent with Seiberg's quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N = 2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.