We present ground-based and textit{Swift} observations of iPTF16fnl, a likely tidal disruption event (TDE) discovered by the intermediate Palomar Transient Factory (iPTF) survey at 66.6 Mpc. The lightcurve of the object peaked at absolute $M_g=-17.2$ mag. The maximum bolometric luminosity (from optical and UV) was $L_p~simeq~(1.0,pm,0.15) times 10^{43}$ 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 $tausimeq 15$ days. The X-ray shows a marginal detection at $L_X=2.4^{1.9}_{-1.1}times 10^{39}$ erg/s (textit{Swift} X-ray Telescope). No radio counterpart was detected down to 3$sigma$, providing upper limits for monochromatic radio luminosity of $ u L_{ u} < 2.3times10^{36}$ erg/s and $ u L_{ u}<1.7times 10^{37}$ erg/s (VLA, 6.1 and 22 GHz). The blackbody temperature, obtained from combined textit{Swift} UV and optical photometry, shows a constant value of 19,000 K. The transient spectrum at peak is characterized by broad He II and H$alpha$ emission lines, with an FWHM of about 14,000 km/s and 10,000 km/s respectively. He I lines are also detected at $lambdalambda$ 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 $sim$650 Myr 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.
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