Results. The light curve of SN 2009E is less luminous than that of SN 1987A and the other members of this class, and the maximum light curve peak is reached at a slightly later epoch than in SN 1987A. Late-time photometric observations suggest that SN 2009E ejected about 0.04 M-circle dot of Ni-56, which is the smallest Ni-56 mass in our sample of 1987A-like events. Modelling the observations with a radiation hydrodynamics code, we infer for SN 2009E a kinetic plus thermal energy of about 0.6 foe, an initial radius of similar to 7x10(12) cm and an ejected mass of similar to 19 M-circle dot. The photospheric spectra show a number of narrow (v approximate to 1800 km s(-1)) metal lines, with unusually strong Ba II lines. The nebular spectrum displays narrow emission lines of H, Na I, [Ca II] and [O I], with the [O I] feature being relatively strong compared to the [Ca II] doublet. The overall spectroscopic evolution is reminiscent of that of the faint Ni-56-poor type II-plateau supernovae. This suggests that SN 2009E belongs to the low-luminosity, low Ni-56 mass, low-energy tail in the distribution of the 1987A-like objects in the same manner as SN 1997D and similar events represent the faint tail in the distribution of physical properties for normal type II-plateau supernovae.