We have studied the submillimetre (submm) properties of the following classes of nearinfrared (NIR)-selected massive galaxies at high redshifts: BzK-selected star-forming galaxies (BzKs); distant red galaxies (DRGs); and extremely red objects (EROs). We used the SCUBA HAlf Degree Extragalactic Survey (SHADES), the largest uniform submm survey to date. Partial overlap of SIRIUS/NIR images and SHADES in SXDF has allowed us to identify 4 submm-bright NIR-selected galaxies, which are detected in the mid-infrared, 24 μm, and the radio, 1.4GHz. We find that all of our submm-bright NIR-selected galaxies satisfy the BzK selection criteria, i.e. BzK ≡ (z−K)AB−(B− z)AB ≥ −0.2, except for one galaxy whose B − z and z −K colours are however close to the BzK colour boundary. Two of the submm-bright NIR-selected galaxies satisfy all of the selection criteria we considered, i.e. they belong to the BzK-DRG-ERO overlapping population, or ‘extremely red’ BzKs. Although these extremely red BzKs are rare (0.25 arcmin−2), up to 20% of this population could be submm galaxies. This fraction is significantly higher than that found for other galaxy populations studied here. Via a stacking analysis, we have detected the 850-μm flux of submm-faint BzKs and EROs in our SCUBA maps. While the contribution of z ~ 2 BzKs to the submm background is about 10–15% and similar to that from EROs typically at z ~1, BzKs have a higher fraction (~ 30%) of submm flux in resolved sources compared with EROs and submm sources as a whole. From the SED fitting analysis for both submmbright and submm-faint BzKs, we found no clear signature that submm-bright BzKs are experiencing a specifically luminous evolutionary phase, compared with submmfaint BzKs. An alternative explanation might be that submm-bright BzKs are more massive than submm-faint ones.