Trump's travel ban, which doesn't include travellers from the United Kingdom, is despite a wealth of evidence that the virus is being transmitted within US communities, not just by travellers.
Hamish Pepper, fixed-income and currency strategist at Harbour Asset Management, said a clarification that the ban doesn't include trade with Europe provided a little relief.
"The kiwi continues to be surprisingly resilient given the environment we're in - a poor risk sentiment environment - and volatility has picked up materially," Pepper said.
While the US dollar and US Treasuries retain some status as safe havens, simply because of the liquidity of those markets, there has been a flight to other havens such as Japan and Switzerland, he said.
The kiwi has dropped 12 per cent year-to-date against the yen compared with only 7 per cent against the greenback.
The next significant event for markets to navigate will be the European Central Bank's meeting tonight, New Zealand time.
Pepper said expectations are mixed, with some expecting no change in the ECB's deposit rate, which is already negative 0.5 per cent, while others expect a very small cut, perhaps to negative 0.6 per cent.
"But really, the focus is on what they might be able to do via their various lending programmes," he said.
For example, the ECB might target lending into particularly vulnerable parts of the economy such as small businesses.
"Out of the small amount of powder that they have that's still dry, they might be able to get some impact."
The ECB is likely to call on governments to spend more, particularly Germany, where maintaining a budget surplus has been paramount – Germany recorded a record 13.5 billion euro surplus in 2019.
"Perhaps this is the classic fear event that this historical resistance to meaningful fiscal stimulus changes," Pepper said.
"It will definitely be something the ECB will continue to push for because it's a far more effective tool."
The New Zealand dollar was trading at 96.84 Australian cents at 5pm, from 96.47 cents late yesterday. It was at 48.79 British pence from 48.65, at 55.31 euro cents from 55.47, at 64.71 yen from 65.82, and at 4.3638 Chinese yuan from 4.3679.
The bid price on the two-year swap rate eased to 0.7218 per cent from 0.7593 yesterday while the 10-year swaps climbed to 1.0600 per cent from 1.0375 per cent.