The wavelength dependence of the extinction of Type Ia SN 2014J in the nearby galaxy M82 has been measured using UV to near-IR photometry obtained with the Hubble Space Telescope, the Nordic Optical Telescope, and the Mount Abu Infrared Telescope. This is the first time that the reddening of an SN Ia is characterized over the full wavelength range of 0.2-2 {mu}m. A total-to-selective extinction, R_V_>= 3.1, is ruled out with high significance. The best fit at maximum using a Galactic type extinction law yields R_V_=1.4+/-0.1. The observed reddening of SN 2014J is also compatible with a power-law extinction, A_{lambda}_/A_V_=({lambda}/{lambda}_V_)^p^ as expected from multiple scattering of light, with p=-2.1+/-0.1. After correcting for differences in reddening, SN 2014J appears to be very similar to SN 2011fe over the 14 broadband filter light curves used in our study.