A brief statement from Moore's publicist Pat Kingsley gave no reason for the split.
However, their friends said work pressures of work and lengthy periods filming on different sides of the world had taken their toll on the 10- year marriage.
No divorce has yet been filed in the Los Angeles Superior Court by the couple, and Ms Kingsley would not be drawn on whether such a move was planned.
She also refused to comment about custody of the couple's three daughters.
Ms Moore's sister, Carolyn Sneed, also refused to say anything about the split.
She said: "It's true, but I sure can't say anything about it. It's Demi's wish, she's asked me not to say anything."
But a friend of Mr Willis told the New York Daily Post: "They spent too much time away from each other, and they were leading separate lives."
Another friend told the New York Daily News: "I think they came to a hard decision. They intend to do it amicably, but that remains to be seen."
In Britain Julia Cole, spokeswoman for the relationship advice service Relate, said it was unlikely the couple had made a sudden decision to part.
She said: "Four in 10 marriages in this country, and an even higher number in America, end in divorce, and it is clearly a very painful experience which usually takes a long time, people don't just come to a quick decision."
Enforced time apart caused by the demands of work could put an unbearable strain on a marriage, she added.Reuse content