Guests sat in tightly-packed chairs which did not appear to be two metres apart, with some of those who have since tested positive sitting close together.
The pair had been seen without masks at the Rose Garden event last Saturday where Mr Trump announced he would be nominating Amy Coney Barrett as his Supreme Court pick.
Several other attendees at the event - former presidential adviser Kellyanne Conway, Senator Mike Lee, Senator Thom Tillis, Notre Dame University president John Jenkins, and an unnamed journalist - have also tested positive.
Hundreds of people were there, and some were seen hugging one another, after the president announced his nomination.
Several top aides and close advisers also attended a small celebration in the Diplomatic Room of the White House afterwards.
There is now speculation the ceremony could become a "superspreader" event, with fears more attendees and close contacts could test positive in the coming days.
The incubation period of the virus is between one to 14 days, although on average people will start to develop symptoms after five to six days.
On Friday, Ms Conway announced she had the virus and had "mild symptoms".
At the event, she was pictured sat behind the first lady and in front of Mr Jenkins, who both tested positive.
Footage also shows her standing close to attorney general William Barr, while neither of them are wearing masks, and leaning in to whisper something to him.
Later, she shakes hands with another guest.
Video has also emerged of Mr Lee enthusiastically hugging other attendees and holding his mask in his hand.
Mr Jenkins, in an email to others at Notre Dame University announcing his positive test, admitted he had not worn a mask and shaken hands with a number of people in the Rose Garden.
He added that he had been tested before attending and was "told that it was safe to remove our masks".
Meanwhile, Alex Azar - the country's top health official - was seen at the event fist-bumping without a mask on, according to CNN.