We present a serendipitous detection of the infrared-bright supernova remnant (SNR) B0104-72.3 in the Small Magellanic Cloud by the Infrared Camera (IRC) onboard AKARI. An elongated, partially complete shell is detected in all four observed IRC bands covering 2.6-15 um. The infrared shell surrounds radio, optical, and X-ray emission associated with the SNR and is probably a radiative SNR shell. This is the first detection of a SNR shell in this near/mid-infrared waveband in the Small Magellanic Cloud. The IRC color indicates that the infrared emission might be from shocked H2 molecules with some possible contributions from ionic lines. We conclude that B0104-72.3 is a middle-aged SNR interacting with molecular clouds, similar to the Galactic SNR IC 443. Our results highlight the potential of AKARI IRC observations in studying SNRs, especially for diagnosing SNR shocks.