Schools were closed and a clean-up operation was underway in Ladispoli, a coastal town west of Rome where the whirlwind hit on Sunday evening.
"It came in from the sea and swept through the town centre. There were fishing boats in the harbour that were moved over 100 metres," the town's mayor, Crescenzo Paliotta, told reporters.
The Indian victim, identified in media reports as farm labourer Surinder Singh, died after being struck by a piece of masonry blown off the edge of an apartment building, Paliotta said.
The other victim was a pensioner who was hit by a falling tree in the small town of Cesano, north of the capital.
The tornado struck as Italy continues to grapple with the damage done to central regions by three powerful earthquakes in just over two months.
A new wave of violent storms was forecast for southern Italy on Monday and authorities in Florence issued a potential flood alert with torrential rain having left the River Arno in danger of bursting its banks.