"In the next couple of days there's going to be a stop to those flights. Those people who maybe still can get out will be getting out," Garwood said.
David Green, of Coatesville, played and coached a hockey team in Italy and only returned there on February 23 for the second half of the season.
Living in the Piedmont region of northern Italy, items like flour, sugar, tinned beans, oil and toilet paper were becoming non-existent, he said.
Red tape had also been placed on the floor of the supermarket to ensure people kept one metre apart from each other.
Public morale was pretty good given the circumstances, Green said, but it could change now given the country had entered the lockdown phase.
"Ask me in a couple of weeks how I'm coping - it might be a different story," he said.
Nicky Meo, another Kiwi in Italy, said authorities appeared to be ramping up their enforcement of the lockdown.
She told Newstalk ZB's Mike Hosking she now needs to carry a stamped permission slip every time they drive to work.
"They seem to be saying they'll do road checks, and if you're outside your zone you'll be fined or imprisoned, so they're making it quite clear they mean it."
Most Italians are broadly supportive of the restrictions and are willing to put up with the inconvenience they cause, Meo said.
"People are afraid, and they're saddened by it, and if you speak to elderly people, they're frightened by it. They want it to go away and they want it to stop."