Microwave has been regarded as a promising technique to break hard igneous rocks. However, there is no criterion to evaluate the ease with which commonly found hard rocks can be fractured by microwave. In this study, 15 hard rocks were treated by a 2.45 GHz single mode microwave cavity at 3 kW for 1 min. The effect of rock properties including the average grain size, the volume inhomogeneity coefficient, the effective dielectric loss factor and the initial P-wave velocity on the P-wave velocity reduction (which is defined as the microwave fracturability index-MFI) was investigated. The first three parameters can be obtained from the petrographic images whereas the last one is easy to assess. The results found positive linear relationships between MFI and the average grain size, the effective dielectric loss factor and the initial P-wave velocity, and a negative linear relationship between MFI and the volume inhomogeneity coefficient. In addition, the study revealed that the most significant factors according the entropy weight method are the effective dielectric loss factor and the average grain size, followed by the volume inhomogeneity coefficient, and finally the initial P-wave velocity. A multi-parameter linear regression model for MFI of igneous rocks was proposed and validated. This work provides an easy and straightforward method to assess the microwave fracturability of a specific rock based on petrographic photomicrographs and P-wave velocity measurement.