During the 1960s, there were many municipal mergers across Norway due to the work of the Schei Committee.

[9] During the 1960s, there were many municipal mergers across Norway due to the work of the Schei Committee.

The first element is kvenna which is the plural genitive case of kona which means "wife" or "woman".

At the time of the municipal dissolution, it was part of the Hitra prestegjeld and the Sør-Fosen prosti (deanery) in the Diocese of Nidaros.

The municipal council (Herredsstyre) of Kvenvær was made up of representatives that were elected to four year terms.