China's manufacturing purchasing managers' index, one of the first official economic indicators published since the coronavirus outbreak, fell to 35.7 in February, a record low, and down from 50 in January.
Last week, US Federal Reserve chairman Jay Powell said the US central bank would "act as appropriate" to support growth.
This helped the S&P 500 pare earlier losses to close down 0.8 per cent after being down as much as 3 per cent.
Finance Minister Grant Robertson, speaking on TVNZ's Q&A programme on Sunday, said he does not expect New Zealand to fall into recession.
"The information that we have today is that there won't be one, that's the advice that we are getting," he said.
"We'll have very low, if any, growth, in the first quarter, in the second quarter, perhaps some growth.
"But this moves fast. That prediction could be revised in the coming weeks," he said.
Bank of New Zealand senior markets strategist Jason Wong said the New Zealand dollar could fall further if the situation worsens.
"The longer that this continues, there will be more downside," he said.
Greg Smith, head of research at Fat Prophets, said fear was running high with the virus continuing to spread globally.
By 11.20 am the sharemarket's NZX50 index was down by 366 points, or 3.2 per cent, at 10,896.
"The first case of coronavirus in New Zealand has investors pretty worried," said Hamilton Hinden Greene director Grant Williamson.
Investors were not just dumping shares with exposure to China.
By mid-morning Ryman Healthcare was down 4.3 per cent at $14.60 while Mercury NZ was down 4.7 per cent at $4.56.
Meanwhile, Synlait Milk shed 4.2 per cent to $5.75 and A2 Milk was down 3.4 per cent at $15.75.
Air New Zealand lost 5.5 per cent, trading at $2.145 and Auckland International Airport dropped 5.5 per cent to $7.44.
"We had a build-up of sellers over the weekend and they came into the market first thing this morning," Williamson said.
"We might see some bargain hunting coming through later. It will depend on how the Australian and Asian markets perform today," said Williamson.
One of the few stocks to be unscathed was SkyCity Entertainment Group, which was unchanged at 3.20.
Overall, however, there's not a lot of volume and not a lot of buying support, he said.
On the potential for a rate cut, Kiwibank senior portfolio manager Ross Weston said the market is pricing 33 basis points of rate cuts by March, 54 by June and a total of 67 basis points over the next year, which is almost three rate cuts.
The central bank's monetary policy committee's OCR review is on March 25.
- Additional reporting, BusinessDesk