We report the results of our spectrophotometric monitoring campaign for AT~2017be in NGC~2537. Its lightcurve reveals a fast rise to an optical maximum, followed by a plateau lasting about 30 days, and finally a fast decline. Its absolute peak magnitude ($M_{r}$ $simeq$ $-$12 $rm{mag}$) is fainter than that of core-collapse supernovae, and is consistent with those of supernova impostors and other Intermediate-Luminosity Optical Transients. The quasi-bolometric lightcurve peaks at $sim$ 2 $times$ 10$^{40}$ erg s$^{-1}$, and the late-time photometry allows us to constrain an ejected $^{56}$Ni mass of $sim$ 8 $times$ 10$^{-4}$msun. The spectra of AT~2017be show minor evolution over the observational period, a relatively blue continuum showing at early phases, which becomes redder with time. A prominent H$alpha$ emission line always dominates over other Balmer lines. Weak Fe {sc ii} features, Ca~{sc ii} H$&$K and the Ca {sc ii} NIR triplet are also visible, while P-Cygni absorption troughs are found in a high resolution spectrum. In addition, the [Ca~{sc ii}] $lambda$7291,7324 doublet is visible in all spectra. This feature is typical of Intermediate-Luminosity Red Transients (ILRTs), similar to SN~2008S. The relatively shallow archival Spitzer data are not particularly constraining. On the other hand, a non-detection in deeper near-infrared HST images disfavours a massive Luminous Blue Variable eruption as the origin for AT~2017be. As has been suggested for other ILRTs, we propose that AT~2017be is a candidate for a weak electron-capture supernova explosion of a super-asymptotic giant branch star, still embedded in a thick dusty envelope.