In this paper, a fixed-switching-frequency modulated model predictive control (M2PC) is established for a two-level three-phase voltage source inverter (VSI) working in an islanded AC microgrid. These small-scale power systems are composed by two or more VSIs which interface DGs, controlling the voltage amplitude and frequency in the system, and simultaneously sharing the load active and reactive power. Generally, these operational characteristics are achieved using hierarchical linear control loops, but with challenging limitations such as slow transient reaction to disturbances and high proneness to be affected by parameter modifications. Model predictive control may solve these issues. Nevertheless, the most used and developed predictive control scheme, the finite-set model predictive control (FS-MPC), presents the drawback of having the harmonic spectrum spread over all the frequencies. This brings issues with coupling between the different hierarchical control levels of the whole microgrid system, and eventually, when designing the filters for main-grid connection. This paper aims to solve these issues by developing the fixed-switching-frequency M2PC working with higher-level control loops for operation in an islanded AC microgrid. These advantages are proved in an AC microgrid configuration where methodology for paralleling multiple M2PC-regulated VSIs is described, with rapid transient response, inherent stability, and fully decentralised operation of individual VSIs, achieving proper load power sharing, eliminating circular currents, and proper waveforms for output currents and capacitor voltages. All these achievements have been confirmed via simulation and experimental verification.