The reigning IBF, WBO and WBA (Super) heavyweight champion met the Prince of Wales at a Commonwealth Day service at Westminster Abbey 16 days ago.
On Wednesday, Prince Charles was diagnosed with the Covid-19 virus with Clarence House announcing the 71-year-old is in ‘good health’ after showing mild symptoms.
Joshua meanwhile has not shown any symptoms of the virus but is now following government guidelines by remaining at home.
A spokesman for Joshua said: “Anthony is at home following government guidelines set out by the Prime Minster to avoid going out, he is fit and well.
"He wishes everyone effected a speedy recovery and a huge thank you to all the front line key workers.”
Joshua is scheduled to defend his world titles against Kubrat Pulev at the Tottenham Hotspur Stadium on June 20 - his first fight back on home soil since knocking out Alexander Povetkin at Wembley Stadium in September 2018.
However, with the coronavirus epidemic forcing cancellations and postponements across the boxing calendar, that fight could also come under threat with Eddie Hearn revealing last week a provisional backup date in July has already been agreed.
Elsewhere, a trilogy fight between WBC champion Tyson Fury and Deontay Wilder is also likely to be postponed. Originally slated for July 18, promoter Bob Arum has now suggested an October date is more likely - a change that would end hopes of Fury and Joshua meeting in a unification bout in 2020.