The observation is reported by scientists using the Hubble Space Telescope (HST).
Although the black hole is headed roughly in our direction, it is at a "safe" distance, 6,000 to 9,000 light-years away, in the direction of the constellation Scorpius.
The object's velocity has been measured at more than 400,000 kilometres per hour, good evidence say the astronomers that it is the accelerated "debris" of a stellar explosion, or supernova.
"This is the first black hole found to be moving fast through the plane of our galaxy," says Felix Mirabel of the French Atomic Energy Commission and the Institute for Astronomy and Space Physics of Argentina. "This discovery is exciting because it shows the link of a black hole to a supernova."
Even though, by definition, black holes swallow light, the runaway object can be studied by looking at the effect it has on its companion star, which somehow survived the supernova blast.
Images from the HST of the companion star have been combined with other data to measure the black hole's motion through the Milky Way's plane.
The black hole, designated GRO J1655-40, is snacking on the companion, pulling gas off the star and slowly eroding it to feed its own mass.
This process makes blowtorch-like jets that stream away from the black hole at a significant fraction of the speed of light. Astronomers call this a "microquasar", meaning that it is a scaled-down model of the monster black holes at the cores of extremely active galaxies, called quasars.
This is the second such mircroquasar discovered in the Milky Way.