Cui Tiankai, China's newly-appointed ambassador to Japan, said Hu's trip would "certainly produce important and far-reaching consequences".
On Wednesday the Shenzhen departed from its base in the southern port of Zhanjiang and was scheduled to arrive in Japan next week for a four-day visit, China's state-run Xinhua news agency reported.
The port call is supposed to be reciprocated by Japan's navy under plans agreed to by the countries' defence ministers in August.
Wen Jiabao, the Chinese premier, told the Japanese prime minister, Yasuo Fukuda, on the sidelines of a South-East Asian summit in Singapore on Tuesday that relations were "at a historical stage of development and a very important turning point".
China says it hopes the visit will have a
"positive effect" on ties
Ties between the neighbours have been strained by disputes over territory, oil resources and Japan's wartime past.
The Shenzhen's first stop will be in Tokyo where Japan's Maritime Self-Defence Force will hold a ceremony, according to the Japanese defence ministry.
Its crew is also scheduled to visit Japan's naval headquarters in Tokyo, and then the ship will make a call at Yokosuka, a port at the entrance to Tokyo Bay which also has the largest US naval base outside the United States.
The Shenzhen will be open visits by the Japanese public, Xinhua said.
China hopes the visit "will have a positive effect on the development of the relationship between the two countries and their defence departments", a spokesman for the foreign ministry in Beijing said.
Military relations between China and Japan are a sensitive issue.
Japan's invasion and occupation of much of China in the 1930s and 1940s left a lasting legacy of bitterness and mistrust.
Warming ties notwithstanding, Japan has expressed concerns about China's surging military spending in recent years, saying China needs to be more transparent about its ambitions.