On 2016 June 22, 2E 1613.5-5053, the puzzling central compact object in supernova remnant RCW 103, emitted a magnetar-like burst. Using Directors Discretionary Time, we observed 2E 1613.5-5053 with the Hubble Space Telescope (WFC3/IR) and we report here on the detection of a previously unseen infrared counterpart. In observations taken on 2016 July 4 and August 11, we detect a new source ($m_mathrm{F110W} = 26.3$ AB mag and $m_mathrm{F160W} = 24.2$ AB mag) at the Chandra position of 2E 1613.5-5053 which was not detected in HST/NICMOS images from 2002 August 15 and October 8 to a depth of 24.5 AB mag (F110W) and 25.5 AB mag (F160W). We show that these deep IR observations rule out the possibility of an accreting binary but mimic IR emission properties of magnetars and isolated neutron stars. The presence or absence of a low-mass fallback disk cannot be confirmed from our observations.