Aims. To investigate the physical nature of the afterglow emission. We report on the photometric, spectroscopic and polarimetric observations of the optical afterglow of Gamma-Ray Burst (GRB) 030328 detected by HETE-2. Methods. Photometric, spectroscopic and polarimetric monitoring of the optical afterglow. Results. Photometry, collected at 7 different telescopes, shows that a smoothly broken powerlaw decay, with indices α 1 = 0.76 ± 0.03, α 2 = 1.50 ± 0.07 and a break at t b = 0.48 ± 0.03 days after the GRB, provides the best fit of the optical afterglow decline. This shape is interpreted as due to collimated emission, for which we determine a jet opening angle θ jet ∼ 3.• 2. An achromatic bump starting around ∼0.2 d after the GRB is possibly marginally detected in the optical light curves. Optical spectroscopy shows the presence of two rest-frame ultraviolet metal absorption systems at z = 1.5216 ± 0.0006 and at z = 1.295 ± 0.001, the former likely associated with the GRB host galaxy. Analysis of the absorption lines at z = 1.5216 suggests that the host of this GRB may be a Damped Lyman-α Absorber. The optical V-band afterglow appears polarized, with P = (2.4 ± 0.6)% and θ = 170• ± 7• , suggesting an asymmetric blastwave expansion. An X-ray-to-optical spectral flux distribution of the GRB 030328 afterglow was obtained at 0.78 days after the GRB and fitted using a broken powerlaw, with an optical spectral slope β opt = 0.47 ± 0.15, and an X-ray slope β X = 1.0 ± 0.2. Conclusions. The discussion of the results in the context of the "fireball model" shows that the preferred scenario for this afterglow is collimated structured jet with fixed opening angle in a homogeneous medium. Observatory (Australia), the 1m Sampurnanand telescope at the ARIES observatory (India), and the 1 m NOFS telescope of USNO in Flagstaff (USA).