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.
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 the first presidential TV debate with Democratic rival Joe Biden in Ohio on Tuesday. Some of Mr Trump's family members who attended the debate were seen not wearing masks.
Mr Trump has mostly spurned mask-wearing and has often been pictured not socially distanced with aides or others during official engagements.
Mr Trump's physician, Sean Conley, released a statement, saying the president and the first lady were "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.
What do you think?