This paper studies the optimal operation of internet data centers (IDCs) in microgrid environments. The proposed model is to minimize the IDC microgrid operation cost, which consists of the operation cost of onsite generations, cost of purchasing power from the main grid, cost due to the repeated charging and discharging of onsite energy storage system (ESS), and the cost due to IDC workload shedding. Both preventive and corrective operation solutions, including power purchase from the main grid, onsite generation dispatch, as well as ESS and IDC workload scheduling are provided for provisioning IDC workloads while considering credible islanding scenarios of the IDC microgrid. Demand response capability of the IDC microgrid is achieved through the proposed optimal solution. The use of ESS for facilitating electricity load shifting is further analyzed via a sensitivity study for minimizing the operation cost of IDC microgrid. Numerical simulations demonstrate the effectiveness of the proposed optimal operation model for IDC microgrid.