In a statement, Schneider said that the 63-year-old star, who had previously battled alcoholism, was sober at the time of his death, but was suffering from anxiety and depression and "was not yet ready to share publicly" his struggle with the debilitating disease.
Williams was found dead at his home in Tiburon, northern California on Monday. A preliminary coroner's report attributed his death to asphyxiation caused by hanging.
Tributes soon flooded in from his co-stars, fellow filmmakers and figures from beyond the entertainment world, including the Prince of Wales and President Barack Obama, who described the Oscar-winner as "one of a kind".
"Since his passing, all of us who loved Robin have found some solace in the tremendous outpouring of affection and admiration for him from the millions of people whose lives he touched,"
Schneider wrote. "Robin's sobriety was intact and he was brave as he struggled with his own battles of depression, anxiety as well as the early stages of Parkinson's disease, which he was not yet ready to share publicly.
"It is our hope in the wake of Robin's tragic passing, that others will find the strength to seek the care and support they need to treat whatever battles they are facing so they may feel less afraid."
Williams made his name as a stand-up comedian and as the star of the popular sitcom Mork and Mindy, which ran from 1978 to 1982. He went on to earn Academy Award nominations for his dramatic performances in Good Morning, Vietnam (1987); Dead Poets Society (1989) and The Fisher King (1991), finally winning an Oscar for his supporting role in 1997's Good Will Hunting.
The actor, who spoke openly about his past problems with alcoholism and cocaine addiction, was married three times and had three children. He and Schneider, a graphic designer, wed in October 2011.
Williams's daughter, 25-year-old Zelda, released a statement earlier this week saying he "was always warm, even in his darkest moments,"
She added: "While I'll never, ever understand how he could be loved so deeply and not find it in his heart to stay, there's minor comfort in knowing our grief and loss, in some small way, is shared with millions."