Dwarf galaxies are dark matter-dominated and therefore promising targets for the search for weakly interacting massive particles (WIMPs), which are well-known candidates for dark matter. Annihilation of WIMPs produce ultra-relativistic cosmic-ray electrons and positrons that emit synchrotron radiation in the presence of magnetic fields. For typical magnetic field strengths (few G) and O(GeV-TeV) WIMP masses (and thus typical electron energies of the same order) this emission peaks at hundreds of MHz. Here, we use the non-detection of 150-MHz radio continuum emission from the dwarf spheroidal galaxy 'Canes Venatici I' with the LOw-Frequency ARray (LO-FAR) to derive constraints on the annihilation cross section of WIMPs into primary electron-positron and other fundamental particle-antiparticle pairs. In this first-of-its-kind LOFAR study, we obtain new constraints on annihilating WIMP dark matter (DM). Using conservative estimates for the magnetic field strengths and diffusion coefficients, we obtain limits that are comparable with those by the Fermi Large Area Telescope (Fermi-LAT) using gamma-ray observations. Assuming s-wave annihilation and WIMPs making up 100% of the DM density, our limits exclude several thermal WIMP realisations in the [2, 20]-GeV mass range. A more ambitious multi-wavelength and multi-target LOFAR study could improve these limits by a few orders of magnitude.