We present ZTF18aaqjovh (SN 2018bvw), a high-velocity ("broad-lined") stripped-envelope (Type Ic) supernova (Ic-BL SN) discovered in the Zwicky Transient Facility one-day cadence survey. ZTF18aaqjovh shares a number of features in common with engine-driven explosions: the photospheric velocity and the shape of the optical light curve are very similar to those of the Type Ic-BL SN 1998bw, which was associated with a low-luminosity gamma-ray burst (LLGRB) and had relativistic ejecta. However, the radio luminosity of ZTF18aaqjovh is almost two orders of magnitude fainter than that of SN 1998bw at the same velocity phase, and the shock velocity is at most mildly relativistic (v=0.06-0.4c). A search of high-energy catalogs reveals no compelling gamma-ray burst (GRB) counterpart to ZTF18aaqjovh, and the limit on the prompt GRB luminosity of L_{gamma},iso_~1.6x10^48^erg/s excludes a classical GRB but not an LLGRB. Altogether, ZTF18aaqjovh represents another transition event between engine-driven SNe associated with GRBs and "ordinary" Ic-BL SNe.