The increasing integration of renewable energy resources (RERs) and the expansion of multi-microgrid systems have transformed the operational condition of power systems. Respectively, the high-amount installation of RERs could result in the volatile changes exchanged-power of local systems, when their power generation drops suddenly. Nevertheless, the available ramp-up power for compensating the supply-demand gap in the power system could be limited due to the operational constraints of power networks and generation units. As a result, in this article, a transactive flexible-ramp-up-management-mechanism is offered in order to enable system operators to exploit the scheduling of microgrid systems with the aim of ensuring power requirements of the multi-microgrid system meet the flexible-ramp-up constraints. Therefore, the mechanism would result in the efficient rescheduling of local flexible resources in a multi-microgrid distribution system in order to address the ramp-up constraints in the system. The offered mechanism limits the information exchange between microgrids and the system operator to transactive control signals and accumulated power exchanges to impede privacy concerns of independently operated entities. Lastly, the recommended mechanism is implemented on the IEEE-37-bus test system, where, its effectiveness in addressing the overall system flexible-ramp-up limitations is investigated.