It said Trump and Vice President Mike Pence have since tested negative for the virus and remain in good health.
It marked the latest coronavirus scare for the president, and the first known instance where a person who has come in close proximity to the president has tested positive since several people present at his private Florida club were diagnosed with COVID-19 in early March.
The person tested positive on Wednesday, the White House said.
White House spokesman Hogan Gidley said in a statement, We were recently notified by the White House Medical Unit that a member of the United States Military, who works on the White House campus, has tested positive for Coronavirus."
He added, "The President and the Vice President have since tested negative for the virus and they remain in great health. A person familiar with the matter said the member of the military who tested positive was one of the president's valets. The person spoke on condition of anonymity because they were not authorized to discuss the matter publicly.
CNN first reported the news, saying that Donald Trump was upset when learning about it Wednesday, and that the personal valet, not identified, exhibited symptoms Wednesday morning.
According to the report, Trump, Pence and other senior staffers are being tested weekly for the coronavirus.
Members of the US Navy are assigned to the White House to assist the first family, thus interacting frequently with them.
The White House instituted safety protocols nearly two months ago, including frequent temperature checks. Last month it began administering rapid COVID-19 tests to all those in close proximity to the president, with staffers being tested about once a week.
Several valets cater to the president and his guests at the White House, both in the West Wing and in the White House residence.
Today, US President Donald Trump and his Russian counterpart Vladimir Putin discussed issues of COVID-19 and arms control during a phone conversation, the White House said.
In the phone call to commemorate the 75th anniversary of Victory in Europe Day, the two leaders discussed progress on defeating the coronavirus pandemic, and Trump said his country is ready to provide assistance to Russia, according to a White House statement on Thursday, Xinhua news agency reported.
"President Trump reaffirmed that the United States is committed to effective arms control that includes not only Russia, but also China, and looks forward to future discussions to avoid a costly arms race," said the statement.
China has repeatedly reiterated that it has no intention of participating in the so-called trilateral arms control negotiations with the United States and Russia.
In 2010, Washington and Moscow signed the New Strategic Arms Reduction Treaty (New START), which stipulates the limits to the numbers of deployed nuclear warheads and strategic delivery systems by both. The New START, the last remaining nuclear arms control treaty in force between the two nuclear superpowers, will expire on February 5, 2021.
The agreement can be extended for at most five years with the consent of the two countries. Russia has expressed willingness to extend the treaty, while the Trump administration has yet to officially reply.