We report on the photometric, spectroscopic and polarimetric, monitoring of the optical afterglow of Gamma-Ray Burst (GRB) 030328 detected by HETE-2. Photometry, collected at 7 different telescopes, shows that a smoothly broken powerlaw decay, with indices alpha_1 = 0.76 +/- 0.03, alpha_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 theta_{jet} of about 3.2 degrees. 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-alpha Absorber. The optical V-band afterglow appears polarized, with P= (2.4 +/- 0.6) % and theta = (170 +/- 7) degrees, 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 beta_{opt} = 0.47 +/- 0.15, and an X-ray slope beta_{X} = 1.0 +/- 0.2. The discussion of these 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.
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