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 66.6 Mpc. 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 similar or equal to (1.0 +/- 0.15) x 10(43) erg s(-1), 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 proportional to e(-(t-t0)/T), where t(0) = 57631.0 (MJD) and tau similar or equal to 15 days. The X-ray shows a marginal detection at L-X = 2.4(-1.1)(1.9) x 10(39) erg s(-1) (Swift X-ray Telescope). No radio counterpart was detected down to 3s, providing upper limits for monochromatic radio luminosities of nu L-nu < 2.3 x 10(36) erg s(-1) and nLn < 1.7 x 10(37) erg s(-1) (Very Large Array, 6.1 and 22 GHz). The blackbody temperature, obtained from combined 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 Ha emission lines, with FWHMs of about 14,000 km s(-1) and 10,000 km s(-1), respectively. He. I 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 similar to 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.