The mood was hardly helped by the World Health Organization declaring the virus a pandemic the same evening.
But Mr Trump's 30-day ban on travel to America from most European countries triggered new record falls in markets on Thursday.
With the global economy already struggling to avoid a recession, it dealt another sharp blow to confidence.
The US is not alone in imposing travel restrictions. India on Wednesday stopped issuing tourist visas. But WHO recommendations are clear: restricting movement of people and goods "is ineffective in most situations and may divert resources from other interventions", as well as interrupting "needed aid and technical support".
It is far from clear, moreover, whether Mr Trump's ban will slow the US spread of the virus. While the president said a number of new clusters there were "seeded by travellers from Europe", Covid-19 is already being spread between Americans who have had no connection with countries with high infection rates.
Excluding the UK and Ireland from the travel ban, too, is puzzling.
They lag behind most west European countries in infection rates per head of population, but are on a similar trajectory. Far more potentially effective than banning travel would have been steps to address the severe shortage of virus testing kits in the US.
One of the worst results of the president's move is to drive a wedge between North Atlantic partners just when international co-ordination is most needed.
Brussels said it "disapproved" of a US decision taken "unilaterally and without consultation", a diplomatic way of saying it was seething.
Market concerns over the economic fallout were compounded by ECB president Christine Lagarde whose ill-judged comments in a press conference undermined a new stimulus package.
European shares had their worst day on record, losing 10 per cent of their value. The UK's FTSE 100 index plunged 11 per cent, its bleakest day since Black Monday in 1987. Only after the Federal Reserve flooded the market with liquidity did US equities recover some of an intraday loss that had peaked at 8 per cent.
Businesses and investors have been looking to policymakers to revive a global economy that was already slowing before the onset of coronavirus. The White House's announcement will instead have a chilling effect on transatlantic commerce, affecting 3,500 flights a week and up to 800,000 passengers, according to Bernstein.
European airline stocks plunged by up to one-fifth, with US counterparts not far behind, as the industry faces its worst downturn since the 9/11 attacks. Travel and leisure stocks from cruise companies to hotels and amusement parks were also hit hard.
The dramatic reaction to Mr Trump's statement highlights the need for policy responses to the virus to be proportionate, co-ordinated, and guided by the best scientific advice.
Yet one of the most disturbing elements of the president's address was its appeal to nationalism.
That the president no longer dismisses the virus as a "Democratic hoax" is a step forward.
But as well as suggesting Covid-19 had been "seeded" by travellers from Europe — who picked it up from China — he insisted the US was fighting a "foreign virus". Associating disease with outsiders is an old practice that rarely ends well.
