We have mapped the J=1->0 line of SiO in a 1 DEG * 12 ARCMIN (l*b) region around the Galactic center (GC) with an angular resolution of 2' (~ 4 pc). In contrast to the spatial distribution of other high dipole moment molecules like CS, whose emission is nearly uniform, the SiO emission is very fragmented and it is only associated with some molecular clouds. In particular, it is remarkable that the SiO emission closely follows the non-thermal radio arc in the GC. The SiO clouds are more extended than the beam with typical sizes between 4 and 20 pc. High angular resolution (26') mapping in the J=2->1 line of SiO toward the molecular clouds in Sgr B2 and Sgr A shows that the SiO emission is relatively smooth with structures of typically 2 pc. From the line intensities of the J=2->1, J=3->2 and J=5->4 transitions of SiO we derive H_2 densities for these clouds of a few 10^4 cm^-3. The SiO fractional abundances are ~10^-9 for the SiO clouds and <~10^-10 for the other molecular clouds in the GC. The characteristics (size and H_2 densities) of the SiO emission in the GC are completely different from those observed in the Galactic disk, where the SiO emission arises from much smaller regions with larger H_2 densities. We briefly discuss the implications of the SiO emission in the molecular clouds of the GC. We conclude that the particular chemistry in these clouds is probably related to large scale fast shocks occurring in the Galactic center region.