She said there was "overwhelming" evidence that North Korea was to blame, and urged Pyongyang to halt its "policy of belligerence".
Mrs Clinton was speaking in South Korea at the end of an Asian tour.
North Korea denies it was responsible, and has warned of retaliation if action is taken against it.
After an international investigation produced proof that the ship, the Cheonan, was hit by a North Korean torpedo, South Korea announced a package of measures, including a halt to most trade. It is also seeking action via the United Nations Security Council.
The North then announced, late on Tuesday, that it was cutting all ties with the South. It has also banned South Korean ships and planes from its territory.
South Korean Foreign Minister Yu Myung-Hwan told a joint news conference he and Mrs Clinton had agreed that North Korea should take responsibility for the sinking of the Cheonan, torpedoed on 26 March with the loss of 46 lives.
"This was an unacceptable provocation by North Korea and the international community has a responsibility and a duty to respond," Mrs Clinton said.
The incident required "a strong but measured response," she said.
Before going to Seoul, Mrs Clinton had two days of discussions in Beijing with her Chinese counterparts.
She has been pressing China to join the international condemnation but Beijing is taking a cautious line, calling for restraint.
"I believe that the Chinese understand the seriousness of this issue and are willing to listen to the concerns expressed by both South Korea and the United States," Mrs Clinton said on Wednesday.
"We expect to be working with China as we move forward in fashioning a response."
Chinese Vice-Foreign Minister Zhang Zhijun earlier said his country was still evaluating information on the sinking of the Cheonan.
"We have always believed that dialogue is better than confrontation," he added.