The 64-year-old Black Sabbath singer, who has previously struggled with addiction, admitted in a message on his Facebook page earlier this month that he had fallen off the wagon.
Speaking on her US television chatshow The Talk, she said: “It’s our business, we’re dealing with it, we’re not getting divorced.
“Am I happy? No. Am I upset? Yes, I am devastated right now.”
The star said she had not realised her husband was using prescription drugs, adding: “We shall deal with it, this too shall pass.”
Earlier this month, Ozzy apologised to his family for his “insane behaviour” after reports the couple, were living separately.