This paper is based on 2MASS photometry (JHKs magnitudes) of 1172 Be stars. The observed mean intrinsic colours have been derived with aid of two-colour diagrams for Be stars of luminosity classes Ie-IIe, IIIe and IVe-Ve. The obtained results are the first determinations of their intrinsic colours in the astronomical literature. The smoothed infrared colours are compared with those obtained for "normal" B stars. Several two-colour diagrams and plots of observed and smoothed intrinsic colour versus spectral type of luminosity classes Ie-IIe, IIIe and IVe-Ve are presented. Generally the determined infrared intrinsic colours of Be stars (V − J)0, (V − H)0, and (V − Ks)o differ substantially from those of "normal" B stars. It is found that the intrinsic colours of B stars are generally bluer than Be stars of corresponding spectral type and luminosity class. The mean absolute visual magnitude Mv of 528 Be stars for luminosity classes Iae, Ibe-Iabe, IIe, IIIe and IVe-Ve is derived from HIPPARCOS parallaxes. The Mv calibration is compared with the existing ones. The Be stars are generally brighter than "normal" B stars of corresponding spectral types.