HD 106906 is a young, binary stellar system, located in the Lower Centaurus Crux (LCC) group. This system is unique among discovered systems in that it contains an asymmetrical debris disk, as well as an 11 M$_{Jup}$ planet companion, at a separation of $sim$735 AU. Only a handful of other systems are known to contain both a disk and directly imaged planet, where HD 106906 is the only one in which the planet has apparently been scattered. The debris disk is nearly edge on, and extends roughly to $>$500 AU, where previous studies with HST have shown the outer regions to have high asymmetry. To better understand the structure and composition of the disk, we have performed a deep polarimetric study of HD 106906s asymmetrical debris disk using newly obtained $H$-, $J$-, and $K1$-band polarimetric data from the Gemini Planet Imager (GPI). An empirical analysis of our data supports a disk that is asymmetrical in surface brightness and structure, where fitting an inclined ring model to the disk spine suggests that the disk may be highly eccentric ($egtrsim0.16$). A comparison of the disk flux with the stellar flux in each band suggests a blue color that also does not significantly vary across the disk. We discuss these results in terms of possible sources of asymmetry, where we find that dynamical interaction with the planet companion, HD 106906b, is a likely candidate.