We study the submillimetre (submm) properties of the following near-infrared (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. Since BzKs are expected to include obscured star-forming galaxies at 1.4 < z < 2.5, it is possible that the submm galaxies are a sub-group of BzKs. We identified 4 BzKs as submm galaxies within 93 arcmin2 by using high resolution radio images. This indicates that only ~20% of submm galaxies are BzKs. However, this fraction is consistent with the assumption that the most of submm galaxies at 1.4 < z < 2.5 are BzKs, considering the redshift distribution, radio-detection rate and observed K-band magnitudes of submm galaxies. We found no submm detections for EROs which are clearly non-BzKs. We identify two submm-bright NIR-selected galaxies, which satisfy all the selection criteria we adopt; 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), about 10% of this population could be submm galaxies. With a stacking analysis, we detected the 850-μm flux of submm-faint BzKs and EROs in our SCUBA maps. While the contribution from BzKs at z ~ 2 to 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 than EROs and submm sources as a whole do. Therefore, submm flux of BzKs seems to be biased high. From the SED fitting using an evolutionary model of starbursts with radiative transfer, submm-bright BzKs are found to have the stellar mass of >5 × 1010M⊙ with the luminosity of >3 × 1012L⊙. From an average SED of submm-faint BzKs having similar B − z and z − K colours to submm-bright ones, we suggest that submm-bright BzKs are more massive than submm-faint ones.