During the Edo period, the area of present-day Kanna was part of the tenryō territory administered directly by the Tokugawa shogunate in Kōzuke Province.

Kanna has a mayor-council form of government with a directly elected mayor and a unicameral town council of 8 members.

Kanna, together with the city of Fujioka and village of Ueno contributes two members to the Gunma Prefectural Assembly.

In terms of national politics, the town is part of Gunma 4th district of the lower house of the Diet of Japan.

The town has one public high school operated by the Gunma Prefectural Board of Education.