The discourse in integrating social and financial functions of Islamic financial institution has emerged as an intellectual critique since the practice of Islamic finance has arguably deviated from the moral expectation of Islamic economy. This argument is further supported by the advent of the interest of combining Islamic finance with impact investing, which should have been in the endogenous facet if Islamic finance since its very beginning. We found several of research papers with theories that Islamic financial and economic institutions, as distinct organisations, require a distinct management framework to be able to achieve their multidimensional purposes. This paper argues that a hybrid organisational management framework could be the most appropriate existing framework to be utilized regarding mission drifts and dysfunctional effects that might happen within such organisations. Hence, this paper provides notions for leaders to develop hybrid organisation culture in terms of time needed for leaders to develop selective criterion in hiring, different types of organisational structures, and the need of a new set of parameters.