This paper reports on Monte Carlo simulation results for future measurements of the moduli of time-like proton electromagnetic form factors, | GE| and | GM| , using the p¯ p→ μ+μ- reaction at P ¯ ANDA (FAIR). The electromagnetic form factors are fundamental quantities parameterizing the electric and magnetic structure of hadrons. This work estimates the statistical and total accuracy with which the form factors can be measured at P ¯ ANDA , using an analysis of simulated data within the PandaRoot software framework. The most crucial background channel is p¯ p→ π+π-, due to the very similar behavior of muons and pions in the detector. The suppression factors are evaluated for this and all other relevant background channels at different values of antiproton beam momentum. The signal/background separation is based on a multivariate analysis, using the Boosted Decision Trees method. An expected background subtraction is included in this study, based on realistic angular distributions of the background contribution. Systematic uncertainties are considered and the relative total uncertainties of the form factor measurements are presented.