  HD 106906 is a 15 Myr old short-period (49 days) spectroscopic binary that
hosts a wide-separation (737 au) planetary-mass ($\sim11\,M_{\rm Jup}$) common
proper motion companion, HD 106906 b. Additionally, a circumbinary debris disk
is resolved at optical and near-infrared wavelengths that exhibits a
significant asymmetry at wide separations that may be driven by gravitational
perturbations from the planet. In this study we present the first detection of
orbital motion of HD 106906 b using Hubble Space Telescope images spanning a 14
yr period. We achieve high astrometric precision by cross-registering the
locations of background stars with the Gaia astrometric catalog, providing the
subpixel location of HD 106906 that is either saturated or obscured by
coronagraphic optical elements. We measure a statistically significant
$31.8\pm7.0$ mas eastward motion of the planet between the two most
constraining measurements taken in 2004 and 2017. This motion enables a
measurement of the inclination between the orbit of the planet and the inner
debris disk of either $36_{-14}^{+27}$ deg or $44_{-14}^{+27}$ deg, depending
on the true orientation of the orbit of the planet. There is a strong negative
correlation between periastron and mutual inclination; orbits with smaller
periastra are more misaligned with the disk plane. With a periastron of
$510_{-320}^{+480}$ au, HD 106906 b is likely detached from the planetary
region within 100 au radius, showing that a Planet Nine-like architecture can
be established very early in the evolution of a planetary system.
