The heavyweight champion, 30, met the Prince of Wales, 71, at the Commonwealth Day service just 16 days ago.
The royal family member remains in “good health” following his diagnosis on Monday night.
But as Joshua was alongside the 71-year-old just over two weeks ago, he will remain at home in isolation.
A spokesman for the heavyweight champion confirmed he has not shown any signs of coronavirus.
They said: “Anthony Joshua 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 sage. Shout out to everyone on the front-line.
“We see you, we appreciate you, we thank you and we’re in awe of you.”
Joshua is scheduled to fight Kubrat Pulev at the Tottenham Hotspur Stadium on 20 June.