Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasistatic and equilibrium behavior of the spin-ice lattice. Here, we study the eigenmode dynamics of such defects in a square lattice consisting of stadiumlike thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitatively analyze monopoles and strings that can be measured experimentally.