We present ground-based and Swift observations of iPTF16fnl, a likely tidal disruption event (TDE) discovered by the intermediate Palomar Transient Factory (iPTF) survey at 66.6Mpc. The light curve of the object peaked at an absolute mag M_g_=-17.2. The maximum bolometric luminosity (from optical and UV) was L_p_~(1.0+/-0.15)x10^43^erg/s, an order of magnitude fainter than any other optical TDE discovered so far. The luminosity in the first 60 days is consistent with an exponential decay, with L{propto}e^-(t-t_0_)/{tau}^, where t_0_=57631.0 (MJD) and {tau}~15 days. The X-ray shows a marginal detection at L_X_=2.4_-1.1_^1.9^x10^39^erg/s (Swift X-ray Telescope). No radio counterpart was detected down to 3{sigma}, providing upper limits for monochromatic radio luminosities of {nu}L_{nu}_<2.3x10^36^erg/s and {nu}L_{nu}_<1.7x10^37^erg/s (Very Large Array, 6.1 and 22GHz). The blackbody temperature, obtained from combined Swift UV and optical photometry, shows a constant value of 19000K. The transient spectrum at peak is characterized by broad HeII and H{alpha} emission lines, with FWHMs of about 14000km/s and 10000km/s, respectively. HeI lines are also detected at {lambda}{lambda}5875 and 6678. The spectrum of the host is dominated by strong Balmer absorption lines, which are consistent with a post-starburst (E+A) galaxy with an age of ~650Myr and solar metallicity. The characteristics of iPTF16fnl make it an outlier on both luminosity and decay timescales, as compared to other optically selected TDEs. The discovery of such a faint optical event suggests a higher rate of tidal disruptions, as low-luminosity events may have gone unnoticed in previous searches.