In 2016 we carried out a Swift monitoring program to track the X-ray hardness variability of eight type-I AGN over a year. The purpose of this monitoring was to find intense obscuration events in AGN, and thereby study them by triggering joint XMM-Newton, NuSTAR, and HST observations. We successfully accomplished this for NGC 3783 in December 2016. We found heavy X-ray absorption produced by an obscuring outflow in this AGN. As a result of this obscuration, interesting absorption features appear in the UV and X-ray spectra, which are not present in the previous epochs. Namely, the obscuration produces broad and blue-shifted UV absorption lines of Ly$alpha$, C IV, and N V, together with a new high-ionisation component producing Fe XXV and Fe XXVI absorption lines. In soft X-rays, only narrow emission lines stand out above the diminished continuum as they are not absorbed by the obscurer. Our analysis shows that the obscurer partially covers the central source with a column density of few $10^{23}$ cm$^{-2}$, outflowing with a velocity of few thousand km s$^{-1}$. The obscuration in NGC 3783 is variable and lasts for about a month. Unlike the commonly-seen warm-absorber winds at pc-scale distances from the black hole, the eclipsing wind in NGC 3783 is located at about 10 light days. Our results suggest the obscuration is produced by an inhomogeneous and clumpy medium, consistent with clouds in the base of a radiatively-driven disk wind at the outer broad-line region of the AGN.