Context. Obscured active galactic nuclei (AGN) represent a significant fraction of the entire AGN population, especially at high redshift (∼70% at z=3-5). They are often characterized by the presence of large gas and dust reservoirs that are thought to sustain and possibly obscure vigorous star formation processes that make these objects shine at far-IR and submillimeter wavelengths. Studying the physical properties of obscured AGN and their host galaxies is crucial to shedding light on the early stages of a massive system lifetime. Aims. We aim to investigate the contribution of the interstellar medium (ISM) to the obscuration of quasars in a sample of distant highly star forming galaxies and to unveil their morphological and kinematics properties. Methods. We exploit Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 4 observations of the continuum (∼2.1mm) and high-J CO emission of a sample of six X-ray selected, far-IR detected galaxies hosting an obscured AGN at z spec > 2.5 in the 7 Ms Chandra Deep Field-South (CDF-S). We measured the masses and sizes of the dust and molecular gas by fitting the images, visibilities, and spectra, and we derived the gas density and column density on the basis of a uniform sphere geometry. Finally, we compared the measured column densities with those derived from the Chandra X-ray spectra. Results. We detected both the continuum and line emission for three sources for which we measured both the flux density and size. For the undetected sources, we derived an upper limit on the flux density from the root mean square (rms) of the images. We found that the detected galaxies are rich in gas and dust (molecular gas mass in the range <0.5 -2.7 × 10 10 M for α CO = 0.8 and up to ∼ 2 × 10 11 M for α CO = 6.5, and dust mass <0.9 -4.9 × 10 8 M ) and generally compact (gas major axis 2.1-3.0 kpc, dust major axis 1.4-2.7 kpc). The column densities associated with the ISM are on the order of 10 23−24 cm −2 , which is comparable with those derived from the X-ray spectra. For the detected sources we also derived dynamical masses in the range 0.8 -3.7 × 10 10 M . Conclusions. We conclude that the ISM of high redshift galaxies can substantially contribute to nuclear obscuration up to the Compton-thick (> 10 24 cm −2 ) regime. In addition, we found that all the detected sources show a velocity gradient reminding one rotating system, even though two of them show peculiar features in their morphology that can be associated with a chaotic, possibly merging, structure.