Context. Low-and intermediate-mass stars at the asymptotic giant branch (AGB) are known to be prevalent dust providers to galaxies, replenishing the surrounding medium with molecules and dust grains. However, the mechanisms responsible for the formation and acceleration of dust in the cool extended atmospheres of AGB stars are still open to debate. Aims. We present visible polarimetric imaging observations of the oxygen-rich AGB star IK Tau obtained with the high-resolution polarimetric imager VLT/SPHERE-ZIMPOL at post-maximum light (phase 0.27) as well as high-spectral resolution long-baseline interferometric observations with the AMBER instrument at the Very Large Telescope Interferometer (VLTI). We aim to spatially resolve the dust and molecule formation regions, and to investigate their physical and chemical properties within a few stellar radii of IK Tau. Methods. IK Tau was observed with VLT/SPHERE-ZIMPOL at three wavelengths in the pseudo-continuum (645, 748, and 820 nm), in the Hα line at 656.3 nm, and in the TiO band at 717 nm. The VLTI/AMBER observations were carried out in the wavelength region of the CO first overtone lines near 2.3 µm with a spectral resolution of 12 000. Results. The excellent polarimetric imaging capabilities of SPHERE-ZIMPOL have allowed us to spatially resolve clumpy dust clouds at 20-50 mas from the central star, which corresponds to 2-5 R when combined with a central star's angular diameter of 20.7±1.53 mas measured with VLTI/AMBER. The diffuse, asymmetric dust emission extends out to ∼73 R . We find that the TiO emission extends to 150 mas (15 R ). The AMBER data in the individual CO lines also suggest a molecular outer atmosphere extending to ∼1.5 R . The results of our 2-D Monte Carlo radiative transfer modelling of dust clumps suggest that the polarized intensity and degree of linear polarization can be reasonably explained by small-sized (0.1 µm) grains of Al 2 O 3 , MgSiO 3 , or Mg 2 SiO 4 in an optically thin shell (τ 550 nm =0.5±0.1) with an inner and outer boundary radius of 3.5 R and 25 R , respectively. The observed clumpy structures can be reproduced by a density enhancement of a factor of 3.0±0.5. However, the model still predicts the total intensity profiles to be too narrow compared to the observed data, which may be due to the TiO emission and/or grains other than homogeneous, filled spheres. Conclusions. IK Tau's mass-loss rate is 20 to 50 times higher than the previously studied AGB stars W Hya, R Dor, and o Cet. Nevertheless, our observations of IK Tau revealed that clumpy dust formation occurs close to the star as seen in those low mass-rate AGB stars.