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Ms Clinton's announcement came a day after Mr Obama's camp said he would launch a campaign swing with chat show queen Oprah Winfrey, and just 37 days before first presidential nominating contests in Iowa.
"Madame President of the United States ... it's an extraordinary thought," said Streisand in a statement issued by the Clinton campaign.
"We truly are in a momentous time, where a woman's potential has no limitations," said the Oscar winning actress and singer.
Streisand is a longtime supporter of former president Bill Clinton, and performed at his inaugural gala in 1993. She has also been savage in her criticisms of President George W Bush.
While celebrity endorsements are keenly sought by presidential candidates, the extent to which they can sway voters is unclear, but it is believed to be minor.
But in the neck-and-neck battle for votes in Iowa, which holds its caucuses on January 3, a shift in sentiment among even small numbers of voters could be significant. © 2007 Australian Broadcasting Corporation