The president, aged 74 and therefore in a high-risk group, announced the news in a tweet. “We will get through this together,” he wrote, reports BBC.
It comes after one of his closest aides tested positive for coronavirus.
Hope Hicks, the 31-year-old adviser to the president, was the closest aide to Mr Trump to test positive so far.
She travelled with him on Air Force One to a TV debate in Ohio this week.
Mr Trump’s physician Sean Conley released a statement, saying the president and the first lady “are both well at this time, and they plan to remain at home within the White House during their convalescence”.
“Rest assured I expect the president to continue carrying out his duties without disruption while recovering, and I will keep you updated on any future developments,” the statement said.
Earlier on Thursday, Mr Trump said he and his wife, who is 50, were going into quarantine after Ms Hicks’s positive test.
He tweeted: “Hope Hicks, who has been working so hard without even taking a small break, has just tested positive for Covid 19. Terrible!
“The First Lady and I are waiting for our test results. In the meantime, we will begin our quarantine process!”
It is not clear how Mr Trump’s positive test will affect arrangements for the second presidential debate, which is scheduled for 15 October in Miami, Florida.