Ozzy, 72, has tested negative for the virus, Sharon said in a post she shared on Twitter and Instagram in the early hours of Tuesday.
Sharon, a co-host of US chat show The Talk, tweeted: “I wanted to share I’ve tested positive for Covid 19. After a brief hospitalisation, I’m now recuperating at a location away from Ozzy (who has tested negative) while The Talk is on scheduled hiatus.
“Everyone please stay safe and healthy.”
The Talk is filmed in Los Angeles, where the Osbournes reportedly live.
Much of the state of California is currently under a stay-at-home order, amid a sharp spike in coronavirus cases.
Sharon’s former X Factor co-judge Nicole Scherzinger was among those who sent messages of support, commenting on Instagram: “Praying for you and love you.”
Sharon’s Covid diagnosis comes days after her The Talk co-host Carrie Ann Inaba also shared that she had tested positive for the virus.
The 52 year old said she is “resting and taking care of myself” following the diagnosis.