The US leader said he and First Lady Melania Trump were now awaiting their own test results after Hope Hicks was infected.
The 31-year-old adviser to the president is the closest aide to Mr Trump to test positive for the disease.
Ms Hicks travelled with Mr Trump on Air Force One to Tuesday’s election debate in Ohio on Tuesday and aboard the presidential helicopter Marine One on Wednesday.
“Hope Hicks, who has been working so hard without even taking a small break, has just tested positive for Covid-19,” the president tweeted.
“The First Lady and I are waiting for our test results. In the meantime, we will begin our quarantine process.”
“I just went for a test and we’ll see what happens,” Mr Trump said earlier during a call-in interview with Fox News Channel’s Sean Hannity on Thursday night.
Ms Hicks is the most senior White House official to test positive for the disease so far.
The president said he expected to have the results back either Thursday night or Friday morning.
The White House had not responded to questions about whether other staffers who spent time with Hicks in recent days will be asked to quarantine.
White House spokesman Judd Deere said Mr Trump “takes the health and safety of himself and everyone who works in support of him and the American people very seriously.”
Ms Hicks is one of the president’s most trusted and longest-serving aides, having worked as spokesperson for his 2016 campaign.
She originally served as White House as communications director, and re-joined the administration this year as an adviser ahead of the election.
Multiple White House staffers have tested positive for the virus, including Katie Miller, Vice President Mike Pence’s press secretary, national security adviser Robert O’Brien.
One of the president’s personal valets also previously tested positive.
After earlier positive cases close to the president, the White House instituted a daily testing regimen for the president’s senior aides.
Anyone who will be in close proximity to the president or vice president is also tested every day, including reporters.