The notion of Sup-hesitant fuzzy quasi-associative ideal in BCI-algebras is introduced, and related properties are investigated. Characterizations of Sup-hesitant fuzzy quasi-associative ideal are provided. Relations between Sup-hesitant fuzzy ideal and Sup-hesitant fuzzy quasi-associative ideal are displayed. Conditions for a Sup-hesitant fuzzy ideal to be a Sup-hesitant fuzzy quasi-associative ideal are provided. Extension property for Sup-hesitant fuzzy quasi-associative ideal is established.