With trading floors ravaged by uncertainty over the tycoon’s plans, many key stock markets also fell, with Wall Street, London, Frankfurt, Paris and Tokyo all lower.
In foreign exchange, the euro hit a six-week high against the dollar at $1.0755.
“The greenback… seems to have been shaken both by the apocalyptic tone set by Trump at his inauguration, and the global protests that greeted the former Apprentice host’s ascension to the highest office in the land,” said Spreadex analyst Connor Campbell.
Trump’s inauguration speech Friday continued his campaign rhetoric, saying “every decision on trade, on taxes, on immigration, on foreign affairs will be made to benefit American workers and American families”.
On Sunday, he vowed to start renegotiating the North American Free-Trade Agreement during upcoming talks with Mexico and Canada.
Doubts about his spending promises also took their toll on the US currency.
“Sellers swiftly exploited the lack of clarity in the speech regarding the proposed fiscal stimulus measures,” said Lukman Otunuga, an analyst at FXTM, predicting more trouble ahead for the greenback.
“The growing threat of Donald Trump’s proposed fiscal stimulus failing to keep up with market expectations may ensure dollar weakness becomes a recurrent theme in the short term,” he said.
The US unit was down more than four percent on the yen from the highs touched late in December. It was also well down against the euro and even against the pound despite concerns about Britain’s exit from the European Union.
“I suspect we’re entering extremely volatile times for the dollar,” Stephen Innes, senior trader at OANDA, said in a note.
Trump last week said the greenback was too strong against China’s yuan and claimed this was “killing” the US economy.
The stronger yen dragged down exporters on Tokyo’s Nikkei, which ended 1.3 percent lower. Takata collapsed again, diving nearly 18 percent on fears of a drawn-out bankruptcy restructuring for the airbag maker at the centre of the biggest-ever auto safety recall.
The embattled stock, which has lost more than half its market value in a week, fell by its daily limit, extending a losing streak to a sixth session.