Inverter-based energy resource is a fast emerging technology for microgrids. Operation of micorgrids with integration of these resources, especially in an islanded operation mode, is challenging. To effectively capture microgrid dynamics and also control these resources in islanded microgrids, a heavy cyber and communication infrastructure is required. This high reliance of microgrids on cyber interfaces makes these systems prone to cyber-disruptions. Hence, the hierarchical control of microgrids, including primary, secondary, and tertiary control, needs to be developed to operate resiliently. This paper shows the vulnerability of microgrid control in the presence of False Data Injection (FDI) attack, which is one type of cyber-disruption. Then, this paper focuses on designing a resilient secondary control based on Unknown Input Observer (UIO) against FDI. The simulation results show the superior performance of the proposed controller over other standard controllers.