In order to understand the internal phenomena in a microwave discharge ion thruster, it is important to measure the distribution of the microwave electric field inside the discharge chamber, which is directly related to the plasma production. In this study, we proposed a novel method of measuring a microwave electric field with an electro-optic (EO) probe based on the Pockels effect. The probe, including a cooling system, contains no metal and can be accessed in the discharge chamber with less disruption to the microwave distribution. This method enables measurement of the electric field profile under ion beam acceleration. We first verified the measurement with the EO probe by a comparison with a finite-difference time domain numerical simulation of the microwave electric field in atmosphere. Second, we showed that the deviations of the reflected microwave power and the beam current were less than 8% due to inserting the EO probe into the ion thruster under ion beam acceleration. Finally, we successfully demonstrated the measurement of the electric-field profile in the ion thruster under ion beam acceleration. These measurements show that the electric field distribution in the thruster dramatically changes in the ion thruster under ion beam acceleration as the propellant mass flow rate increases. These results indicate that this new method using an EO probe can provide a useful guide for improving the propulsion of microwave discharge ion thrusters.