Recent studies of radio data put strong constraints on annihilation cross sections for dark matter. In this article, we provide the first analysis of using M33 radio data in constraining annihilating dark matter. The resulting constraints of annihilation cross sections for some channels are more stringent than that obtained from six years of Fermi Large Area Telescope (Fermi-LAT) gamma-ray observations of the Milky Way dwarf spheroidal satellite galaxies. In particular, the conservative lower limits of dark matter mass annihilating via e⁺e⁻, µ⁺µ⁻, т⁺т⁻ channels are 190, 120 and 70 GeV, respectively, with the thermal relic annihilation cross section. These results are in significant tension with some of the recent quantitative analyses of the AMS-02 and Fermi-LAT data of the Milky Way center. Copyright © 2017 American Physical Society.