Context. Be/X-ray binaries represent the main group of high-mass X-ray binaries. The determination of the astrophysical parameters of the counterparts of these high-energy sources is important for the study of X-ray binary populations in our Galaxy. X-ray observations suggest that SAX J2239.3+6116 is a Be/X-ray binary. However, little is known about the astrophysical parameters of its massive companion. Aims: The main goal of this work is to perform a detailed study of the optical variability of the Be/X-ray binary SAX J2239.3+6116. Methods: We obtained multi-colour BVRI photometry and polarimetry and 4000-7000 Å spectroscopy. The 4000-5000 Å spectra allowed us to determine the spectral type and projected rotational velocity of the optical companion; the 6000-7000 Å spectra, together with the photometric magnitudes, were used to derive the colour excess E(B-V), estimate the distance, and to study the variability of the Hα line. Results: The optical counterpart to SAX J2239.3+6116 is a V = 14.8 B0Ve star located at a distance of 4.9 kpc. The interstellar reddening in the direction of the source is E(B-V) = 1.70 ± 0.03 mag. The monitoring of the Hα line reveals a slow long-term decline of its equivalent width since 2001. The line profile is characterized by a stable double-peak profile with no indication of large-scale distortions. We measured intrinsic optical polarization for the first time. Although somewhat higher than predicted by the models, the optical polarization is consistent with electron scattering in the circumstellar disk. Conclusions: We attribute the long-term decrease in the intensity of the Hα line to the dissipation of the circumstellar disk of the Be star. The longer variability timescales observed in SAX J2239.3+6116 compared to other Be/X-ray binaries may be explained by the wide orbit of the system.