Context. Transitional disks represent a short stage of the evolution of circumstellar material. Studies of dust grains in these objects can provide pivotal information on the mechanisms of planet... Show moreContext. Transitional disks represent a short stage of the evolution of circumstellar material. Studies of dust grains in these objects can provide pivotal information on the mechanisms of planet formation. Dissimilarities in the spatial distribution of small ({$μ$}m-size) and large (mm-size) dust grains have recently been pointed out. Aims: Constraints on the small dust grains can be obtained by imaging the distribution of scattered light at near-infrared wavelengths. We aim at resolving structures in the surface layer of transitional disks (with particular emphasis on the inner 10-50 AU), thus increasing the scarce sample of high-resolution images of these objects. Methods: We obtained VLT/NACO near-IR high-resolution polarimetric differential imaging observations of SAO 206462 (HD 135344B). This technique allows one to image the polarized scattered light from the disk without any occulting mask and to reach an inner working angle of ~{}0.1{Prime}. Results: A face-on disk is detected in H and K$_s$ bands between 0.1{Prime} and 0.9{Prime}. No significant differences are seen between the H and K$_s$ images. In addition to the spiral arms, these new data allow us to resolve for the first time an inner disk cavity for small dust grains. The cavity size ({sime}28 AU) is much smaller than what is inferred for large dust grains from (sub-)mm observations (39 to 50 AU). This discrepancy cannot be ascribed to any resolution effect. Conclusions: The interaction between the disk and potential orbiting companion(s) can explain both the spiral arm structure and the discrepant cavity sizes for small and large dust grains. One planet may be carving out the gas (and, thus, the small grains) at 28 AU, and generating a pressure bump at larger radii (39 AU), which holds back the large grains. We analytically estimate that, in this scenario, a single giant planet (with a mass between 5 and 15 M$_J$) at 17 to 20 AU from the star is consistent with the observed cavity sizes. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, under program number 089.C-0611(A).Reduced data are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/560/A105Show less