The 46-year-old actor was found dead Sunday in his New York City apartment.
In a statement, the family said the "outpouring of love and support" was appreciated. They asked people to respect their privacy.
Hoffman made his career mostly as a character actor, and he was one of the most prolific in the business.
The stage-trained actor's rumpled naturalism made him one of the most admired performers of his generation. He was nominated for Academy Awards four times and won the Oscar for best actor in 2006 for his portrayal of writer Truman Capote in "Capote."
He leaves behind his partner of 15 years, Mimi O'Donnell, and their three children.