"Don tested positive at the start of the week and has been quarantining out at his cabin since the result", the spokesman said.
As it stands, Trump Jr.is now at home in quarantine and is asymptomatic.
Queen, Prince Philip celebrate 73rd wedding anniversary amid England's lockdown
The card was first revealed in a photo shared by the Royal Family social media accounts on Thursday. Their great grandchildren, meanwhile, are isolating at Anmer Hall in Norfolk with their parents.
Bloomberg News previously reported that a number of others who attended a November 3 election party at the White House - including Housing and Urban Development Secretary Ben Carson and Trump campaign adviser David Bossie - also contracted the virus.
The White House has hosted a number of events that eschewed social distancing guidelines, including a crowded Election Night party that Don Jr. attended.
Earlier this month, in the days after the presidential election, Trump's chief of staff, Mark Meadows, told associates that he had coronavirus.
Speaking with Fox News' Laura Ingraham last month, Don Jr. downplayed the severity of the pandemic, saying "the number [of new deaths] is nearly nothing because we have gotten control of this".
Over the summer, his Twitter account was restricted for sharing a video that spread false information about the drug hydroxychloroquine and he shared a Facebook meme spreading doubt about the effectiveness of masks against the coronavirus. Chuck Grassley of Iowa and Sen.