Around 10% of bright low-frequency radio sources observed with the Murchison Widefield Array (MWA) show strong Interplanetary Scintillation (IPS) on timescales of a few seconds, implying that almost all their low-frequency radio emission comes from a compact component less than 0.5 arcsec in angular size. Most of these objects are compact steep-spectrum (CSS) or MHz-peaked spectrum (MPS) radio sources. We have used mid-infrared data from the Wide-field Infrared Survey Explorer (WISE) catalogue to search for the host galaxies of 65 strongly-scintillating MWA sources and compare their properties with those of the overall population of bright low-frequency radio sources. We identified WISE mid-infrared counterparts for 91% of the bright sources in a single 900 square degree MWA field, and found that the hosts of the strongly-scintillating sources were typically at least 1 mag fainter in the WISE W1 (3.4 micron) band than the hosts of weakly-scintillating MWA sources of similar radio flux density. This difference arises mainly because the strongly-scintillating sources are more distant. We estimate that strongly-scintillating MWA sources have a median redshift of z ~ 1.5, and that at least 30% of them are likely to lie at z > 2. The recently-developed wide-field IPS technique therefore has the potential to provide a powerful new tool for identifying high-redshift radio galaxies without the need for radio spectral-index selection.