Bloomberg was the first to report the diagnosis.
The younger Trump is one of several people in Donald Trump's inner circle -- including the president himself -- who has caught the novel coronavirus.
"Don tested positive at the start of the week and has been quarantining out at his cabin since the result," Donald Trump Jr.'s spokesman said in a statement to CNN. "He's been completely asymptomatic so far and is following all medically recommended COVID-19 guidelines."
Earlier Friday, Florida Sen. Rick Scott said he also tested positive for COVID-19 and is in quarantine at his home in the southwestern part of the state.
Scott said he's been self-isolating since last weekend after learning he'd come in contact with a person who tested positive. Initial tests for Scott after the discovery were negative.
"After several negative tests, I learned I was positive for COVID-19," Scott tweeted. "I'm feeling good and experiencing very mild symptoms. I'll be working from home until it's safe for me to return to [Washington, D.C.]
"I remind everyone to be careful and do the right things to protect yourselves and others."
Scott, who is quarantining at his Naples home, is the latest of many Republican politicians to test positive for the coronavirus disease since the summer. Iowa Sen. Chuck Grassley also tested positive this week.
Some of the other GOP leaders who have picked up the virus include President Donald Trump, first lady Melania Trump, their son Barron Trump, White House chief of staff Mark Meadows, party Chairwoman Ronna McDaniel, White House press secretary Kayleigh McEnany, aide Hope Hicks, campaign manager Bill Stepien, former adviser Kellyanne Conway, and Sens. Mike Lee, Ron Johnson and Thom Tillis.
After revealing his test, Scott asked Americans to take proper precautions to limit the spread.
"Wear a mask. Socially distance. Quarantine if you come in contact with someone positive like I did," Scott tweeted. "We will beat this together, but we all must be responsible.
"I want to thank all the incredible healthcare workers who are working around the clock to care for patients."
Scott was governor of Florida between 2011 and 2019.
Andrew Giuliani, son of Trump's personal attorney Rudy Giuliani, also said Friday he has tested positive.
The younger Giuliani has served as a special assistant to Trump.
"I am experiencing mild symptoms, and am following all appropriate protocols, including being in quarantine and conducting contact tracing," he tweeted.