"These activities in the Indian Ocean are directly linked to the stability of the Middle East, on which we rely for natural resources, and are directly linked to our national interests."
The Murasame will join forces with a support ship, which is to set sail on Friday.
Japan has been providing logistical support to US-led forces involved in the war in Afghanistan since 2001, when the mission was suspended last November after the opposition blocked an extension.
The stand down deeply embarrassed Yasuo Fukuda, the Japanese prime minister, and cast doubt on how far Tokyo can back the US in its fight against global terrorism.
The Democratic Party which currently dominates the upper house of Japan's parliament has opposed the mission saying that military operations in Afghanistan did not have the explicit support of the United Nations and could violate pacifist clauses in Japan's constitution.
Earlier this month, the government used its majority in the more powerful lower-house of parliament to push through legislation resuming the naval mission after it was rejected by the upper house.
The law, which gives the mission a one year mandate, limits Japanese vessels to refuelling boats and supplying water not directly involved in combat operations in Afghanistan.
This includes ships used in monitoring and inspecting vessels suspected of links to terrorism or arms smuggling.
The restrictions were aimed at winning over a public wary about violating the spirit of Japan's post-World War II pacifist constitution.