Using the Moon to occult the Sun, the Clementine spacecraft used its navigation cameras to map the inner zodiacal light at optical wavelengths over elongations of 3≲∊≲30° from the Sun. This surface brightness map is then used to infer the spatial distribution of interplanetary dust over heliocentric distances of about 10 solar radii to the orbit of Venus. The averaged ecliptic surface brightness of the zodiacal light falls off as Z(∊)∝∊ -2.45±0.05, which suggests that the dust cross-sectional density nominally falls off as σ( r)∝ r-1.45±0.05. The interplanetary dust also has an albedo of a≃0.1 that is uncertain by a factor of ∼2. Asymmetries of ∼10% are seen in directions east-west and north-south of the Sun, and these may be due the giant planets' secular gravitational perturbations. We apply a simple model that attributes the zodiacal light as due to three dust populations having distinct inclination distributions, namely, dust from asteroids and Jupiter-family comets (JFCs) having characteristic inclinations of i∼7°, dust from Halley-type comets having i∼33°, and an isotropic cloud of dust from Oort Cloud comets. The best-fitting scenario indicates that asteroids + JFCs are the source of about 45% of the optical dust cross section seen in the ecliptic at 1 AU but that at least 89% of the dust cross section enclosed by a 1-AU-radius sphere is of a cometary origin. Each population's radial density variations can also deviate somewhat from the nominal σ( r)∝ r-1.45. When these results are extrapolated out to the asteroid belt, we find an upper limit on the mass of the light-reflecting asteroidal dust that is equivalent to a 12-km asteroid, and a similar extrapolation of the isotropic dust cloud out to Oort Cloud distances yields a mass equivalent to a 30-km comet, although the latter mass is uncertain by orders of magnitude.