"This morning, I lost my husband and my best friend, while the world lost one of its most beloved artists and beautiful human beings. I am utterly heartbroken," Schneider said.
"On behalf of Robin's family, we are asking for privacy during our time of profound grief. As he is remembered, it is our hope the focus will not be on Robin's death, but on the countless moments of joy and laughter he gave to millions."
Williams was found dead of an apparent "suicide due to asphyxia" in his Northern California home around 11:55 a.m. PST on Monday. A statement released by the actor's rep unveiled that he had been "battling severe depression of late."
Zelda Williams, the second of the actor's three children, payed tribute to her father in a Twitter post where she quotes famed french author Antoine De Saint-Exupery.
"I love you. I miss you. I'll try to keep looking up," she added in her post.
William's has also been honored by celebrities including Steve Martin, Rita Wilson, his Mrs. Doubtfire costar Mara Wilson and President Barack Obama on the social media site.
The Oscar-winning actor is survived by Schneider, his third wife, and his three children, Zachary Pym, 31, Zelda Rae, 25, and Cody Alan, 22.