The ministry said the case occurred in Saitama, a prefecture adjacent to Tokyo. Local media reports said the patient was a teen-aged girl who has since recovered.
Government spokesperson Yoshihide Suga, in confirming the report, said on Wednesday that the news was not cause for alarm because the illness is not transmitted directly from person to person.
Japan sees dozens of imported cases of dengue fever each year, mostly tourists who catch the illness while traveling in tropical regions.
The disease, which is transmitted by mosquito, was common in Japan during World War II but was locally eradicated for decades.
Dengue causes symptoms including fever, severe joint pain and headaches. There is no treatment.
Dengue has been spreading in recent years, with 50 million to 100 million dengue infections a year in more than 100 countries. According to the World Health Organisation, before 1970 only nine countries had experienced dengue epidemics. Japan reported 249 cases last year.