A spokesman for the couple said: “At this time Ozzy is not at the marital home.”
The Black Sabbath frontman, 67, has fought a public battle with drug and alcohol addiction throughout their marriage.
He relapsed and this led to divorce rumours in 2013, but Mrs Osbourne, 63, stood by her husband.
Reports suggest their current separation is not due to substance abuse issues.
Various media outlets have reported the rock star has had an affair with a younger hairdresser called Michelle Pugh.
Ms Pugh is a celebrity hairdresser whose clients include Jennifer Lopez and Alicia Silverstone.
A spokesman at Meche, the hair salon where Michelle works, says she has taken some time off for what they described as a “personal emergency.”
The Sun reports that Ozzy had checked into the Beverly Hills Hotel but later left and his whereabouts are unknown.
The Sun quoted an insider as saying: “Jack [Ozzy’s son] tried to get hold of Ozzy because he thinks he might talk some sense into him.
“He and his sisters Kelly and Aimee are worried about him and are a bit shocked by what has gone on.
“But Sharon is in an unforgiving mood and does not want him in the house, so it’s a difficult position.”
Mrs Osbourne, a former judge on ITV’s The X Factor, detailed her reaction to her husband’s relapse in her book, Unbreakable: My New Autobiography.
The star, who is a panellist on daytime US series The Talk, discovered he had relapsed as the couple celebrated 30 years of marriage.
“I would never have imagined our anniversary would be the start of one of the worst periods in our marriage,” she wrote.
Osbourne and his wife met in the 1970s via her father Don Arden, who was managing the heavy metal group at that time.
Mrs Osbourne managed the Birmingham-born rocker before becoming his wife.
The pair wed in 1982 and have three children together: Aimee, Kelly, and Jack.
Osbourne also has three children from his previous marriage.
The Osbourne family found a new level of fame when, with the exception of oldest child Aimee, they appeared in a television series together.
The Osbournes, the popular MTV reality show revolving around their lives, ran from 2002 to 2005 and became an instant hit.
It made the Osbournes household names around the globe.
As recently as last year, the family was in talks for a possible reboot of The Osbournes.