Debris disks are tenuous, dusty belts surrounding main sequence stars generated by collisions between planetesimals. HD 206893 is one of only two stars known to host a directly imaged brown dwarf orbiting interior to its debris ring, in this case at a projected separation of 10.4au. Here we resolve structure in the debris disk around HD 206893 at an angular resolution of 0".6 (24au) and wavelength of 1.3mm with the Atacama Large Millimeter/submillimeter Array (ALMA). We observe a broad disk extending from a radius of <34au to 158±6au. We model the disk with a continuous, gapped, and double power-law model of the surface density profile, and find strong evidence for a local minimum in the surface density distribution near a radius of 70au, likely due to a gap in the disk with an inner radius of 73+5/-9au and width 13+5/-7au. Gapped structure has been observed in four other debris disks — essentially every other debris disk observed with sufficient angular resolution and sensitivity with ALMA — and would be suggestive of an additional planetary-mass companion.