Aims: The intracluster light (ICL) is a faint diffuse stellar component of clusters made of stars that are not bound to individual galaxies. We have carried out a large scale study of this component in the nearby Virgo cluster. Methods: The diffuse light is traced using planetary nebulae (PNe). The surveyed areas were observed with a narrow-band filter centered on the [OIII]λ 5007 Å emission line redshifted to the Virgo cluster distance (the on-band image), and a broad-band filter (the off-band image). For some fields, additional narrow band imaging data corresponding to the Hα emission were also obtained. The PNe are detected in the on-band image due to their strong emission in the [OIII]λ 5007 Å line, but disappear in the off-band image. The contribution of Ly-α emitters at z=3.14 are corrected statistically using blank field surveys, when the Hα image at the field position is not available. Results: We have surveyed a total area of 3.3 square degrees in the Virgo cluster with eleven fields located at different radial distances. Those fields located at smaller radii than 80 arcmin from the cluster center contain most of the detected diffuse light. In this central region of the cluster, the ICL has a surface brightness in the range μB = 28.8-30 mag arsec-2, it is not uniformly distributed, and represents about 7% of the total galaxy light in this area. At distances larger than 80 arcmin the ICL is confined to single fields and individual sub-structures, e.g. in the sub-clump B, the M 60/M 59 group. For several fields at 2 and 3 degrees from the Virgo cluster center we set only upper limits. Conclusions: These results indicate that the ICL is not homogeneously distributed in the Virgo core, and it is concentrated in the high density regions of the Virgo cluster, e.g. the cluster core and other sub-structures. Outside these regions, the ICL is confined within areas of ~100 kpc in size, where tidal effects may be at work. These observational results link the formation of the ICL with the formation history of the most luminous cluster galaxies. Based on data collected with the 2.5 m Isaac Newton Telescope on La Palma, the Subaru telescope, operated by the National Astronomical Observatory of Japan, and the ESO/MPI 2.2 m telescope at La Silla, Chile, operated by ESO during observing runs 62.N-0248 and 70.B-0086(A).