It was founded by Russians in 1861. In 1925, its original name Zelenchuksko-Loovsky (Зеленчукско-Лоовский) was changed to Inzhich-Chukun, the Russified local name of Maly Zelenchuk, as a part of a campaign to remove the names of nobility (Loovsky in this case) from the toponyms.
Inzhich-Chukun was a part of Khabezsky District prior to creation of Abazinsky District in 2006.