Summary: The operator \(L(\cdot)\) of the basic multiple hypergeometric function given by R. K. Yadav et al. [Algebras Groups Geom. 27, No. 1, 97–115 (2010; Zbl 1247.33033)] is used in order to obtain the fractional \(q\)-integral operator \(L(\cdot)\) of the generalized basic hypergeometric function \(_r\phi_s(\cdot)\). Also the \(q\)-Mellin transform for the operator \(L(\cdot)\) is presented. Various interesting special cases, involving \(q\)-special functions, are derived as application of the main result.