At the same time, Italy will lift curbs on travellers from the United States, Canada, Japan and other European Union states if they have a green pass showing they are vaccinated or recently tested negative, the minister wrote on Facebook.
A ban on people arriving from India, Bangladesh and Sri Lanka will remain in place, he added.
The new measures will come into force on Monday, a health ministry spokesman said.
Italy is following in the footsteps of France, Austria and Germany, which have already introduced varying curbs on those entering from Britain.
Britain on Friday said there had been a 79% increase in weekly reported cases of the Delta coronavirus variant, which was first identified in India. The variant now comprises 91% of sequenced cases, Public Health England said.