The heavyweight champion, 30, met the the Prince of Wales, 71, at the Commonwealth Day service just 16 days ago.
The royal remains in “good health” following his diagnosis on Monday night.
But as Joshua met the 71-year-old just over two weeks ago, he will remain at home in isolation.
A spokesperson for the heavyweight champion confirmed he has not shown any signs of coronavirus.
Symptons of the deadly virus – which has claimed 433 lives in the United Kingdom – are believed to appear between two and 11 days.
AJ’s represenative said: “AJ is at home following government guidelines, he is fit and well.
“He wishes everyone affected a speedy recovery and a huge thank you to all the front line key workers.”
Earlier this week, WBA, IBF, WBO and IBO champ Joshua tweeted: “Hi guys, hope everyone’s staying safe.
“It’s humbling to see people giving their everything right now to keep us safe. Shout out to everyone on the front-line.
“We see you, we appreciate you, we thank you and we’re in awe of you.”
AJ is scheduled to fight Kubrat Pulev at the Tottenham Hotspur Stadium on June 20.