We argue that dielectric haloscopes like MADMAX, originally designed for detecting axion dark matter, are also very promising gravitational wave detectors. Operated in resonant mode at frequencies around O(10  GHz), these detectors benefit from enhanced gravitational wave to photon conversion at the surfaces of a stack of thin dielectric disks. Since the gravitational wave is relativistic, there is an additional enhancement of the signal compared to the axion case due to increased conversion probability of gravitational waves to photons in the vacuum between the disks. A gravitational wave search using a dielectric haloscope imposes stringent requirements on the disk thickness and placement, but relaxed requirements on the disk smoothness. An advantage is the possibility of a broadband or hybrid resonant/broadband operation mode, which extends the frequency range down to O(100  MHz). We show that strain sensitivities down to 10−21  Hz−1/2×(10  GHz/f) will be possible in the coming years for the broadband setup, while a resonant setup optimized for gravitational waves could even reach 3×10−23  Hz−1/2×(10  GHz/f) with current technology.