We present ZTF20aajnksq (AT 2020blt), a fast-fading ({Delta}r=2.3mag in {Delta}t=1.3d) red (g-r~0.6mag) and luminous (M_1626{AA}_=-25.9mag) optical transient at z=2.9 discovered by the Zwicky Transient Facility (ZTF). AT 2020blt shares several features in common with afterglows to long-duration gamma-ray bursts (GRBs): (1) an optical light curve well-described by a broken power law with a break at t_j_=1d (observer frame); (2) a luminous (L_0.3-10KeV_=10^46^erg/s) X-ray counterpart; and (3) luminous (L_10GHz_=4x10^31^erg/s/Hz) radio emission. However, no GRB was detected in the 0.74d between the last ZTF nondetection (r>21.36mag) and the first ZTF detection (r=19.60mag), with an upper limit on the isotropic-equivalent gamma-ray energy release of E_{gamma},iso_<7x10^52^erg. AT 2020blt is thus the third afterglow-like transient discovered without a detected GRB counterpart (after PTF11agg and ZTF19abvizsw) and the second (after ZTF19abvizsw) with a redshift measurement. We conclude that the properties of AT2020blt are consistent with a classical (initial Lorentz factor {Gamma}_0_>~100) on-axis GRB that was missed by high-energy satellites. Furthermore, by estimating the rate of transients with light curves similar to that of AT 2020blt in ZTF high-cadence data, we agree with previous results that there is no evidence for an afterglow-like phenomenon that is significantly more common than classical GRBs, such as dirty fireballs. We conclude by discussing the status and future of fast-transient searches in wide-field high-cadence optical surveys.