The high sensitivity of upcoming space-based gravitational wave detectors suggests the possibility that if halo dark matter were composed of primordial black holes (PBHs) with mass between 10(16) g and 10(20) g, the gravitational interaction with detector test masses will lead to a detectable pulse-like signal during the fly-by. For an improved version of the Laser Interferometer Space Antenna with a reduced acceleration noise at the low-end of its frequency spectrum, we find an event rate, with signal-to-noise ratios greater than 5, of similar to a few per decade involving black holes of mass similar to 10(17) g. The detection rate improves significantly for second generation space based interferometers that axe currently envisioned, though these events must be distinguished from those involving perturbations due to near-Earth asteroids. While the presence of primordial black holes below a mass of similar to 10(16) g is now constrained based on the radiation released during their evaporation, the gravitational wave detectors will extend the study of PBHs to a several orders of magnitude higher masses.