The euro was fell to a two-week low of $0.9885 EUR=EBS, within sight of two-decade lows hit earlier this month. It was last down 0.6 per cent at $0.9912.
Sterling, which was down 0.4 per cent, fell to a fresh 37-year low of $1.1304 GBP=D3 even before Putin started speaking.
"The Russia headlines are stealing the thunder from the Fed at least for now," said Societe Generale currency strategist Kenneth Broux.
"A concern about an escalation in the conflict is hurting European currencies. And if the Fed is also hawkish tonight then you could see the losses snowball."
Later on Wednesday, the Federal Reserve is expected to lift interest rates by three-quarters of a percentage point for a third straight time and signal how much further and how fast borrowing costs may need to rise to tame a potentially corrosive outbreak of inflation.
The policy decision, due at 1800 GMT, will mark the latest move in a synchronised policy shift by global central banks that is testing the resilience of the world economy and the ability of countries to manage exchange rate shocks as the value of the dollar soars.
The dollar index is up almost 16 per cent this year and set for its biggest annual jump since 1981.
Analysts said the backdrop of heightened geopolitical uncertainty only added to dollar strength.
"Obviously we have a situation where investors flock to safe havens, and we've also got the anticipation that we are going to see another rate hike from the Federal Reserve today," said Danni Hewson, financial analyst at AJ Bell in London.
"So the dollar was already looking quite punchy and clearly just the proximity to Ukraine of countries in Europe does make people consider what the situation might look like if the war in Ukraine becomes something bigger."
The Australian and New Zealand dollars meanwhile hit multi-year lows on Wednesday. The Aussie AUD=D3 hit a trough of $0.6655, its lowest since June 2020, while the kiwi NZD=D3 fell to $0.5877, its lowest since April 2020.
The rouble tumbled towards 63 against the dollar on Wednesday, scaling more than two-month lows,and Russian stock markets dived around 10 per cent on opening as president Vladimir Putin ordered the country's first military mobilisation since World War Two.
By 0708 GMT, the rouble was 2.6 per cent weaker at 62.18 to the dollar RUBUTSTN=MCX, having dipped as far as 62.7975, its weakest point since 7 July.
It had lost 1.7 per cent to trade at 61.61 to the euro EURRUBTN=MCXand shed 1.5 per cent against the yuan to 8.776 CNYRUBTOM=MCX.
Russian stock indexes were plunging, with energy giants Rosneft ROSN.MM and Gazprom GAZP.MM at one point losing around 12 per cent.
The benchmark rouble-based MOEX index .IMOEX hit its lowest point since 24 February, the day Russia sent tens of thousands of troops into Ukraine.
The index was down 5.5 per cent at 2,094.5 points, earlier reaching a low of 2,002.73 points. The dollar-denominated RTS index .IRTS was down 8 per cent to 1,061.9 points, its lowest point since 27 April.