On Twitter, he cited “the attack from the invisible enemy”, as he calls the virus, and the need to protect the jobs of Americans, but did not give details.
It was not clear what programmes might be affected and whether the president would be able to carry out the order.
Critics say the government is using the pandemic to crack down on immigration.
Immigration has traditionally been a strong campaigning theme for Mr Trump, but has taken a back seat during the pandemic and in the lead-up to the November election.
In light of the attack from the Invisible Enemy, as well as the need to protect the jobs of our GREAT American Citizens, I will be signing an Executive Order to temporarily suspend immigration into the United States!
— Donald J. Trump (@realDonaldTrump) April 21, 2020
Mr Trump’s announcement late on Monday came as the White House argued that the worst of the pandemic was over and the country could begin reopening. The restrictions on people’s movement, implemented by many states to curb the spread of the virus, have paralysed parts of the economy.
Over the past four weeks, more than 20 million Americans have registered for unemployment benefits. That amounts to roughly as many jobs as employers had added over the previous decade.
The US has more than 787,000 confirmed cases of Covid-19 and more than 42,000 deaths, according to a tally by Johns Hopkins University, which is tracking the pandemic globally.
How can the proposals be implemented?
A Trump campaign statement on Tuesday said the move had two functions – to prevent competition for jobs that could add to dole queues and depress wages, and stop imported infections.
It was not immediately clear who could be affected by Mr Trump’s announcement or when such a move could come into force.