The doting grandmother reassured the panel that Minnie was okay, but that the entire family were now isolating.
Following on from the news, Jack Osbourne was inundated with messages from fans asking how his daughter was, and the doting dad has since spoken out.
VIDEO: Jack Osbourne updates fans on daughter Minnie after she tested positive for coronavirus
Taking to Instagram, the TV personality shared a video from inside his home in LA, of Minnie sitting at the table.
"A lot of you are asking how Minnie is. She is doing totally fine," he said.
Jack Osbourne with his daughters and parents Ozzy and Sharon Osbourne
Jack then asked his daughter: "Min, how you doing?" to which she replied: "Fine." "Well, she's getting good," he said.
Minnie is Jack's youngest child. The star is also dad to older daughters Pearl and Andy, who he shares with ex-wife Lisa Stelly.
On Monday, Sharon revealed her surprise at Minnie getting the virus, as the rest of her family tested negative for it.
Jack is a doting dad to his daughters
She said: "She's okay, she's doing good. I don't have it. Her daddy doesn't have it. Her mommy doesn't have it. Her sisters don't. She got it from somebody who works for my son.
"And it just goes to show you, she's three years of age, that children can get Covid."
Doting grandmother Sharon has been spending the majority of the summer with her grandchildren, who joined her on a family holiday in August.
Sharon Osbourne is a proud grandmother to three grandchildren
Sharon adores spending time with her grandchildren, and opened up about the incredible experience of being a grandmother when Pearl was first born in 2012.
She told People: "It's all overwhelming. But in a good way – in a really positive, lovely way.
"You go through every emotion. You go through joy and you thank god that everybody is healthy and happy. You realise how lucky you are. It's like life has gone full cycle in our family."
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