Microtubule-based long-distance transport in eukaryotic cells typically involves the binding of cargo to motors such as highly processive kinesins for unidirectional transport. An open question is whether long-distance transport can occur by mechanisms that do not require specific motor-cargo interactions and high processivity. In addition to conventional cargo such as vesicles, kinesin also shuttles non-motor microtubule-associated proteins (MAPs) to microtubule ends. Computational modeling of a system of a motor and a MAP that do not bind directly with one another unexpectedly revealed the redistribution of the MAP to microtubule plus ends, suggesting an unconventional mode of protein transport. We recapitulated this phenomenon experimentally in a minimal in vitro system using a kinesin-1 protein (K401) and PRC1, a non-motor MAP that binds diffusively on microtubules and shows no detectable binding to K401. Single-molecule imaging revealed unidirectional streams of PRC1 molecules over micron distances along microtubules. Our findings suggest that a stoichiometric excess of K401 can act as a unidirectional barrier to PRC1 diffusion. This effectively \"shepherds\" PRC1 to microtubule plus end without conventional motor-cargo interactions. Remarkably, we found that shepherding occurs with low kinesin processivity. Shepherding by kinesin-1 was also observed with another MAP. These findings reveal a new mechanism of transport for microtubule-bound cargo that does not require high-affinity motor-cargo binding and motor processivity, two principles conventionally invoked for cellular transport.