Pyrochlore oxides possessing "all-in-all-out" spin ordering have attracted burgeoning interest as a rich ground of emergent states. This ordering has two distinct types of magnetic domains (all-in-all-out or all-out-all-in) with broken time-reversal symmetry, and a nontrivial metallic surface state has been theoretically demonstrated to appear at their domain wall. Here, we report on the observation of this metallic conduction at the single all-in-all-out/all-out-all-in magnetic domain wall formed at the heterointerface of two pyrochlore iridates. By utilizing the different magnetoresponses of them with different lanthanide ions, the domain wall is controllably inserted at the heterointerface, the surface state being detected as an anomalous conduction enhancement with a ferroic hysteresis. Our establishment paves the way for further investigation and manipulation of this new type of surface transport.