The effect of electronic correlations on the spin-dependent ballistic transport in Fe/MgO/Fe magnetic tunnel junctions with FeO interface layers is investigated by means of first-principles calculations. The self-interaction correction to the local spin-density approximation (LSDA) is applied to electronic states localized at the FeO layers. With respect to LSDA, the electronic and magnetic properties are significantly changed; e.g. the magnetic moment at the Fe interface is increased by 23%, the conductance is in general decreased, and the tunnel magnetoresistance ratio is reduced by up to 40%. The self-interaction correction is deemed beneficial in transport calculations for systems with localized states, e.g. those with oxide layers.