We have searched for dust in an optical sample of 910 Early-Type Galaxies (ETGs) in the Virgo cluster (447 of which are optically complete at mpg ≤ 18.0), extending also to the dwarf ETGs, using Herschel images at 100, 160, 250, 350 and 500 μm. Dust was found in 52 ETGs (46 are in the optically complete sample), including M87 and another 3 ETGs with strong synchrotron emisssion. Dust is detected in 17% of ellipticals, 41% of lenticulars, and in about 4% of dwarf ETGs. The dust-to-stars mass ratio increases with decreasing optical luminosity, and for some dwarf ETGs reaches values similar to those of the dusty late-type galaxies. Slowly rotating ETGs are more likely to contain dust than fast rotating ones. Only 8 ETGs have both dust and HI, while 39 have only dust and 8 have only HI, surprisingly showing that only rarely dust and HI survive together. ETGs with dust appear to be concentrated in the densest regions of the cluster, while those with HI tend to be at the periphery. ETGs with an X-ray active SMBH are more likely to have dust and vice versa the dusty ETGs are more likely to have an active SMBH.