Topological superconductors are associated with the appearance of Majorana bound states, with promising applications in topologically protected quantum computing. In this Letter, we study a system where a skyrmion crystal is interfaced with a normal metal. Through interfacial exchange coupling, spin fluctuations in the skyrmion crystal mediate an effective electron-electron interaction in the normal metal. We study superconductivity within a weak-coupling approach and solve gap equations both close to the critical temperature and at zero temperature. Special features in the effective electron-electron interaction due to the noncolinearity of the magnetic ground state yield topological superconductivity at the interface.