While urging others to seek help for problems they might be facing,
It was something Williams was "not yet ready" to share publicly, she said.
The actor and comic, who took his own life Tuesday at age 63, had been "brave" as he struggled with that diagnosis as well as with depression and anxiety, Schneider said.
Parkinson's and depression "can go hand in hand," the National Parkinson Foundation said in a statement of its own Tuesday, noting that an NPF study had found that more than half of those with the disease experience clinical depression.
Depression "is part of the disease process itself" and can hurt a person's quality of life even more than the motor impairments that are the most visible part of Parkinson's, the foundation said.
"Stunned to learn Robin had [Parkinson's]," Fox said Thursday on Twitter. "Pretty sure his support for our [foundation] predated his diagnosis. A true friend; I wish him peace."
Williams had in fact sought out help in recent weeks, spending time in a rehab program that his people said was to "fine-tune" his sobriety. The program included, in part, meditation and spiritual work.
"Robin spent so much of his life helping others," Schneider said in her statement. "Whether he was entertaining millions on stage, film or television, our troops on the front lines, or comforting a sick child -- Robin wanted us to laugh and to feel less afraid.
"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. His greatest legacy, besides his three children, is the joy and happiness he offered to others, particularly to those fighting personal battles.
"Robin's sobriety was intact and he was brave as he struggled with his own battles of depression, anxiety as well as 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' three adult children, Zack, Zelda and Cody Williams, released statements Wednesday remembering their father, as did Marsha Garces Williams, the actor's second wife.