Recent observations of gamma rays with the Fermi Large Area Telescope (LAT) in the direction of the inner galaxy revealed a mysterious excess of GeV. Its intensity is significantly above predictions of the standard model of cosmic rays (CRs) generation and propagation with a peak in the spectrum around a few GeV. Popular interpretations of this excess are that it is due to either spherically distributed annihilating dark matter (DM) or an abnormal population of millisecond pulsars. We suggest an alternative explanation of the excess through the CR interactions with molecular clouds in the Galactic Center (GC) region. We assumed that the excess could be imitated by the emission of molecular clouds with depleted density of CRs with energies below ∼10 GeV inside. A novelty of our work is in detailed elaboration of the depletion mechanism of CRs with the mentioned energies through the “barrier” near the cloud edge formed by the self-excited MHD turbulence. This depletion of CRs inside the clouds may be a reason for the deficit of gamma rays from the Central Molecular Zone (CMZ) at energies below a few GeV. This in turn changes the ratio between various emission components at those energies and may potentially absorb the GeV excess by a simple renormalization of key components.