Integrated whole-body PET/MRI provides opportunities to fully take advantage of simultaneously acquired anatomical and functional information. The purpose of this study is to incorporate the MR measured anatomical information in myocardial perfusion (MP) PET image reconstruction and to quantitatively evaluate the reconstructed images. Using the 4D XCAT phantom, we simulated cardiac-gated MP PET data with and without a perfusion defect and the corresponding MR images. Noisy PET sinograms were generated with count levels comparable to patient Rb-82 MP PET measurement. MR images were simulated using the SIMRI simulator, with the MR sequence specified to be 3D T1-weighted as used in a clinical PET/MRI protocol. For each cardiac gate, we applied the closed-form maximum a posteriori (MAP) PET image reconstruction taking the joint-entropy (JE) between intensity of the PET and MR images as the prior. To quantitatively evaluate the reconstructed images, we used the tradeoff between bias and noise on the left ventricle polar map. The contrast recovery ratio was also calculated to quantify the ability to classify the polar maps with and without the MP defect. On the whole polar map and its segments, the activity values estimated from the JE MAP algorithm showed significantly improved noise versus bias tradeoff compared to those from the conventional maximum likelihood algorithm. The JE MAP algorithm also resulted in improved noise versus contrast recovery for the MP defect. To conclude, we demonstrated quantitatively improved performance of the anato-functional JE MAP reconstruction on MP PET imaging with realistic simulation. The reconstruction technique will have promising potential applications especially in the emerging integrated cardiac PET/MR imaging.