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Abstract Fast X-ray transients (FXTs) are a new observational class of phenomena with no clear physical origin. This is at least partially a consequence of limited multiwavelength follow-up of this class of transients in real time. Here we present deep optical (g- andi-band) photometry with Keck, and prompt radio observations with the Very Large Array of FXT 210423 obtained atδt≈ 14–36 days since the X-ray trigger. We use these multiband observations, combined with publicly available data sets, to constrain the presence and physical properties of on-axis and off-axis relativistic jets such as those that can be launched by neutron star mergers and tidal disruption events, which are among the proposed theoretical scenarios of FXTs. Considering a wide range of possible redshiftsz≤ 3.5, circumstellar medium densityn= 10⁻⁶–10⁻¹cm⁻³, and isotropic-equivalent jet kinetic energyE_k,iso= 10⁴⁸–10⁵⁵erg, we find that we can rule out wide jets with opening angleθ_j= 15° viewed within 10° off-axis. For more collimated jets (θ_j= 3°) we can only rule out on-axis (θ_obs= 0°) orientations. This study highlights the constraining power of prompt multiwavelength observations of FXTs discovered in real time by current (e.g., Einstein Probe) and future facilities.