In this paper, we explore the impact of Dark Matter-photon interactions on the CMB angular power spectrum. Using the one-year data release of the Planck satellite, we derive an upper bound on the Dark Matter-photon elastic scattering cross section of sigma(DM-gamma) <= 8 x 10(-31) (m(DM)/GeV) cm(2) (68% CL) if the cross section is constant and a present-day value of sigma(DM-gamma) <= 6 x 10(-40) (m(DM)/GeV) cm(2) (68% CL) if it scales as the temperature squared. For such a limiting cross section, both the B-modes and the T T angular power spectrum are suppressed with respect to Lambda CDM predictions for l >= 500 and l >= 3000 respectively, indicating that forthcoming data from CMB polarisation experiments and Planck could help to constrain and characterise the physics of the dark sector. This essentially initiates a new type of dark matter search that is independent of whether dark matter is annihilating, decaying or asymmetric. Thus, any CMB experiment with the ability to measure the temperature and/or polarisation power spectra at high l should be able to investigate the potential interactions of dark matter and contribute to our fundamental understanding of its nature.