About 10 minutes into trading, the Dow Jones Industrial Average was down 0.7 percent at 27,625.35.
The broad-based S&P 500 shed 1.0 percent to 3,348.65, while the tech-rich Nasdaq Composite Index fell 1.4 percent to 11,174.07.
US stock futures plunged on the Trump announcement early Friday morning, but traded in a range around that lower level for several hours and did not move significantly after the jobs data was released at 1230 GMT.
Analysts on CNBC noted that there is a wide range of possible outcomes for an individual with coronavirus, from very serious afflictions and even death, to an asymptomatic outcome.
There was also speculation the news could improve the odds of fiscal stimulus, potentially boosting stocks.
“The knee-jerk selloff makes sense,” said Briefing.com analyst Patrick O’Hare, who said it is unknowable how the president’s diagnosis will affect the presidential election, ongoing negotiations on fiscal stimulus and a pending Supreme Court nomination.
O’Hare said the fact that the market stabilized after the initial fall shows it is not “catastrophizing” the possible outcomes.
In terms of the jobs data, the United States added a less-than-expected 661,000 jobs in September but the unemployment rate fell to 7.9 percent, the Labor Department said.
The positions gained last month were less than half of the upwardly revised nearly 1.5 million positions added in August, indicating a slowdown in the pace of the employment recovery after business shutdowns beginning in March to stop Covid-19 caused mass layoffs.