The benchmark S&P/ASX200 dropped 57 points, or 0.70 per cent, to 8141.1, while the broader All Ordinaries sunk 57.8 points, or 0.69 per cent, to 8363.1.
Mr Trump has promised to extend tariffs to more countries from April 2, after hitting Canada and Mexico with 25 per cent levies and doubling duties on Chinese goods to 20 per cent.
The president has not yet mentioned Australia.
"We have been ripped-off for decades by nearly every country on earth and we will not let that happen any longer," Mr Trump said in an address to a joint sitting of congress.
Energy stocks posted a third day of losses, giving up 1.7 per cent over the session, as the trade war further tempered global demand expectations and pushed oil prices closer towards $US70 per barrel.
Penfolds owner Treasury Wine Estates was the worst performer on the S&P/ASX200, falling more than 5 per cent after going ex-dividend.
Coles and Woolworths also took a hit after paying dividends to shareholders, dropping 4.4 per cent and 3.9 per cent respectively to $18.89 and $28.72.
The supermarket slump helped drive consumer staples 3.6 per cent lower, the worst performing sector of the day.
Utilities was the only sector to finish in the green, grinding 0.11 per cent higher, but still down more than 2 per cent for the month.
Iron ore giants BHP and Rio Tinto edged slightly higher as China announced new stimulus measures to help achieve its 5 per cent growth target, which it held steady in the face of US tariff pressures.
Iron ore futures in Singapore briefly dropped below $US100 after China confirmed it would cut its crude steel output to adjust to the downturn in its troubled property sector.
Speculation of an expected 50 million metric tonne cut has sent iron ore prices about 6 per cent lower since Thursday.
Australia's economy grew 0.6 per cent in the December quarter, the strongest result in two years and breaking out of a per capita recession for the first time in seven straight quarters.
The improved result was still sluggish, Westpac economist Neha Sharma said.
"While there will be more support from lower interest rates in 2025, the pace of easing is likely to be slow and the response from households is expected to remain fairly muted," Ms Sharma said.
The Australian dollar has rebounded slightly and is buying 62.54 US cents, up from 61.97 US cents a day ago.
ON THE ASX:
* The benchmark S&P/ASX200 index on Monday fell 57 points, or 0.70 per cent, to 8141.1.
* The broader All Ordinaries lost 57.8 points, or 0.69 per cent, to 8363.1.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 62.54 US cents, down from 61.97 US cents at 5pm AEDT on Tuesday
* 93.63 Japanese yen, from 92.56 yen
* 58.82 euro cents, from 59.13 euro cents
* 48.88 British pence, from 48.82 pence
* 110.68 NZ cents, from 110.58 NZ cents
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