The former US secretary of state said she believes a yes vote would be a "loss for both sides" and she is hoping that it does not happen.
Clinton, who is on a tour to promote her memoir Hard Choices and is widely believed to be preparing for a presidential run in 2016, also indicated she was keen for Britain to remain part of the European Union.
"I would hate to have you lose Scotland," she told BBC 2's Newsnight. "I hope that it doesn't happen but I don't have a vote in Scotland. But I would hope it doesn't happen."
She added: "I would think it would be a loss for both sides but, again, I don't have a vote."
Clinton insisted the so-called special relationship between Britain and the US was "worth everything to me and to our country".
She added: "I do think we see the world very similarly."
Asked if Britain's standing would be enhanced or diminished in the United States if it left the European Union, she replied: "Oh, boy you are asking me to cross into dangerous waters, which I will not do."
She added: "Europe needs Britain, in my opinion. I think Britain brings a perspective and an experience that is very important to Europe, especially post-economic crisis. So, Britain will have to decide if they agree with that."
Clinton's intervention on the Scottish referendum debate comes just one week after US president Barack Obama said he believed that the United Kingdom appears to have "worked pretty well".
A spokesman for Yes Scotland said of Clinton's comments: "As she says, the decision about Scotland's future is one for the people of Scotland to make. After a Yes vote, the friendship between Scotland and the United States will flourish to the benefit of both nations."
A Better Together spokesman said: "Hillary Clinton is a figure who is respected right across the world. Like president Obama, she understands that the UK is at its strongest when it works together.
"She has said 'no thanks' to Alex Salmond's attempts to divide the people of Britain. We are grateful for her support."Suggest a correction