"I would hate to have you lose Scotland," said Clinton, widely considered the Democratic front-runner if she enters the 2016 US presidential race.
Her comments came a week after Obama said the United States wanted a "united" partner, but that the Scottish vote was for Scots to decide.
Obama also made it clear he would prefer Britain to stay inside the European Union, saying it was encouraging for Washington to know its ally had "a seat at table in the larger European project".
British Prime Minister David Cameron has promised to try and renegotiate the country's ties with the EU to claw back a range of powers if re-elected next year, and to then give Britons a referendum on whether to remain inside the EU in 2017.
When asked about British membership of the EU, Clinton said "Europe needs Britain." She said she thought Britain brought a perspective that was important to Europe, especially post-economic crisis.
An opinion poll from Thursday showed that support for Scottish independence has risen markedly in the past month with nationalists still behind but gaining ground.