The Solar System is home to a cloud of dust that orbits the Sun and makes its presence known by virtue of scattered light (Zodiacal Light) that can be seen after dusk and before dawn. Within this cloud are bands of dust orbiting near the ecliptic plane, evidenced by an excess of scattered light at discrete ecliptic latitudes. Dedicated dust detectors borne by spacecraft in transit of the solar system have detected few such particles of the appropriate size owing to limited detector aperture and sparsity of the population. Thus, the distribution, origin, and orbital evolution of the dust in these bands remains a mystery. A star camera aboard the Juno spacecraft traveling from Earth to Jupiter recorded interplanetary dust impacts on the spacecraft in numbers sufficient to characterize the spatial distribution of such particles for the first time. The observed distribution is consistent with a primary source of dust particles sharing the Mars orbit plane between Earth and the 4:1 resonance with Jupiter. We propose that the primary distribution is scattered by orbital resonances with Jupiter via the Kozai-Lidov (KL) effect into a secondary population at higher inclination to the ecliptic. The measured dust distribution, occupying a volume uniquely determined by the orbital elements of Mars and KL scattering, accounts for the observed variation of the Zodiacal Light with ecliptic latitude. Our results provide a compelling alternative to the prevailing theory of the origin and evolution of interplanetary dust observed at low ecliptic latitudes.