[3] Copper mining and soapstone quarries were historically significant industries in the municipality.

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

The 952-square-kilometre (368 sq mi) Kvikne parish in the south (population: 664) was merged into Tynset Municipality in Hedmark county and the 201-square-kilometre (78 sq mi) Innset parish in the north (population: 420) was incorporated into Rennebu Municipality in Sør-Trøndelag county.

A few years later in 1970, the border was adjusted again with the Garlia farm (population: 5) being transferred from Tynset to Rennebu.

[7] The municipal council (Herredsstyre) of Kvikne was made up of 13 representatives that were elected to four year terms.