Observations of the extragalactic (z = 0.0141) transient AT 2018cow established a new class of energetic explosions shocking a dense medium, producing luminous emission at millimeter and submillimeter wavelengths. Here we present detailed millimeter- through centimeter-wave observations of a similar transient, ZTF 20acigmel (AT 2020xnd), at z = 0.2433. Using observations from the NOrthern Extended Millimeter Array and the Very Large Array, we model the unusual millimeter and radio emission from AT 2020xnd under several different assumptions and ultimately favor synchrotron radiation from a thermal electron population (relativistic Maxwellian). The thermal electron model implies a fast but subrelativistic (v ≈ 0.3c) shock and a high ambient density (n e ≈ 4 × 103 cm−3) at Δt ≈ 40 days. The X-ray luminosity of L X ≈ 1043 erg s−1 exceeds simple predictions from the radio and UVOIR luminosity and likely has a separate physical origin, such as a central engine. Using the fact that month-long luminous (L ν ≈ 2 × 1030 erg s−1 Hz−1 at 100 GHz) millimeter emission appears to be a generic feature of transients with fast (t 1/2 ≈ 3 days) and luminous (M peak ≈ −21 mag) optical light curves, we estimate the rate at which transients like AT 2018cow and AT 2020xnd will be detected by future wide-field millimeter transient surveys such as CMB-S4 and conclude that energetic explosions in dense environments may represent a significant population of extragalactic transients in the 100 GHz sky.