This paper discusses the challenges faced by cyber-physical microgrids (MGs) due to the inclusion of information and communication technologies in their already complex, multi-layered systems. The work identifies a research gap in modeling and analyzing stealthy intermittent integrity attacks in MGs, which are designed to maximize damage and cancel secondary control objectives. To address this, the paper proposes a nonlinear residual-based observer approach to detect and mitigate such attacks. In order to ensure a stable operation of the MG, the formulation then incorporates stability constraints along with the detection observer. The proposed design is validated through case studies on a MG benchmark with four distributed generators, demonstrating its effectiveness in detecting attacks while satisfying network and stability constraints.