Tests confirmed she was infected with the H5N1 bird flu virus, it said. It did not say how the girl, surnamed Peng, was infected or what she was doing in Hunan.
"The patient is in critical condition, and the health department of Shanxi province is sparing no efforts" to save the girl, the notice said.
All the people who had close contact with the girl were under medical observation, the ministry said, and no one else has been found ill.
The case comes at a worrisome time for authorities as tens of millions of people are on the move between cities and rural hometowns for Chinese New Year, which begins on Jan. 26. The Agricultural Ministry has said it will step up checks before the holiday.
China, which raises more poultry than any other country, has vowed to aggressively fight the virus.
A spokeswoman for the World Health Organization in Beijing said it was informed of the case and was staying in close contact with the Health Ministry.
Earlier this month a 19-year-old woman died from the bird flu virus in a Beijing hospital after contact with ducks in a market in a neighboring province, the first death from bird flu since February last year. The WHO said the case did not appear to signal a new public health threat.
Health officials worry the H5N1 virus could mutate into a form that could spread easily among people.
According to the latest WHO tally, bird flu has killed 248 people worldwide since 2003, including 21 in China. The young girl brings the total number of cases in the country to 32.