Emerging market stocks and the highly sensitive Mexican peso slid to session lows following Trump's early morning post on Twitter that gave no details on the plan.
Representatives for the Office of the U.S. Trade Representative could not be reached for comment.
"Brazil and Argentina have been presiding over a massive devaluation of their currencies, which is not good for our farmers. Therefore, effective immediately, I will restore the Tariffs on all Steel & Aluminum that is shipped into the U.S. from those countries," Trump wrote.
Brazil's President Jair Bolsonaro, an avowed Trump fan who has sought closer U.S. ties, said in local radio interview that he would call his U.S. counterpart, who he was confident would listen to Brazil's concerns.
"Their economy is not comparable with ours, it's many times bigger. I don't see this as retaliation," Bolsonaro said in a radio interview with Brazil's Radio Itatiaia.
"I'm going to call him so that he doesn't penalize us ... Our economy basically comes from commodities, it's what we've got. I hope that he understands ...and I'm almost certain he'll listen to us," he said.
Argentine Production Minister Dante Sica said Trump's announcement was "unexpected" and he was seeking talks with U.S. officials. Additionally, Argentina's Foreign Ministry said it will begin negotiations with the U.S. State Department.
Trump's tweet also urged the Federal Reserve to lower interest rates so countries "no longer take advantage of our strong dollar. Lower Rates & Loosen - Fed!"
Trump has repeatedly urged the U.S. central bank to lower rates to below zero, but Fed policymakers have been reluctant. Fed policy makers hold their next meeting on Dec 10-11.
Pre-market shares in U.S. steelmakers rose on Monday, with United States Steel Corp up 1.2% and AK Steel Holding rising 2.5% before the bell.
In Brazil, steelmakers fell sharply as the market opened but quickly reversed losses. Shares in Brazil's Cia Siderurgica Nacional SA, Usiminas and Gerdau SA were up 1.5%, 1.4% and 0.5% in mid-morning trade, respectively.
Brazil's benchmark Bovespa equities index was up 0.9%. The country's currency, the real, initially fell around 0.5% at the open, nearer to last week's record low. But it recovered to trade stronger at 4.2230 per dollar.
(Writing by Toby Chopra, Hugh Bronstein, Susan Heavey and Gabriel Stargardter; additional reporting by Cassandra Garrison and Maximilian Heath in Buenos Aires, Lisandra Paraguassu in Brasilia, Pedro Fonseca in Rio de Janeiro; Editing by Chizu Nomiyama, Nick Zieminski and David Gregorio)