We present optical and near-infrared photometry and spectroscopy of SN 2009ib, a Type II-P supernova in NGC 1559. This object has moderate brightness, similar to those of the intermediate-luminosity SNe 2008in and 2009N. Its plateau phase is unusually long, lasting for about 130 d after explosion. The spectra are similar to those of the subluminous SN 2002gd, with moderate expansion velocities. We estimate the Ni-56 mass produced as 0.046 +/- A 0.015 M-aS (TM). We determine the distance to SN 2009ib using both the expanding photosphere method (EPM) and the standard candle method. We also apply EPM to SN 1986L, a Type II-P SN that exploded in the same galaxy. Combining the results of different methods, we conclude the distance to NGC 1559 as D = 19.8 +/- A 3.0 Mpc. We examine archival, pre-explosion images of the field taken with the Hubble Space Telescope, and find a faint source at the position of the SN, which has a yellow colour [(V - I)(0) = 0.85 mag]. Assuming it is a single star, we estimate its initial mass as M-ZAMS = 20 M-aS (TM). We also examine the possibility, that instead of the yellow source the progenitor of SN 2009ib is a red supergiant star too faint to be detected. In this case, we estimate the upper limit for the initial zero-age main sequence (ZAMS) mass of the progenitor to be similar to 14-17 M-aS (TM). In addition, we infer the physical properties of the progenitor at the explosion via hydrodynamical modelling of the observables, and estimate the total energy as similar to 0.55 x 10(51) erg, the pre-explosion radius as similar to 400 R-aS (TM), and the ejected envelope mass as similar to 15 M-aS (TM), which implies that the mass of the progenitor before explosion was similar to 16.5-17 M-aS (TM).