We present the first scattered light detections of the HD 106906 debris disk using the Gemini/Gemini Planet Imager in the infrared and Hubble Space Telescope (HST)/Advanced Camera for Surveys in the optical. HD 106906 is a 13 Myr old F5V star in the Sco-Cen association, with a previously detected planet-mass candidate HD 106906b projected 650 AU from the host star. Our observations reveal a near edge-on debris disk that has a central cleared region with radius ∼50 AU, and an outer extent >500 AU. The HST data show that the outer regions are highly asymmetric, resembling the "needle" morphology seen for the HD 15115 debris disk. The planet candidate is oriented ∼21° away from the position angle of the primary's debris disk, strongly suggesting non-coplanarity with the system. We hypothesize that HD 106906b could be dynamically involved in the perturbation of the primary's disk, and investigate whether or not there is evidence for a circumplanetary dust disk or cloud that is either primordial or captured from the primary. We show that both the existing optical properties and near-infrared colors of HD 106906b are weakly consistent with this possibility, motivating future work to test for the observational signatures of dust surrounding the planet.