The low-mass X-ray binary (LMXB) system FIRST J102347.6+003841 hosts a newly born millisecond pulsar (MSP) PSR J1023+0038 that was revealed as the first and only known rotation-powered MSP in a quiescent LMXB. While the system is shown to have an accretion disk before 2002, it remains unclear how the accretion disk has been removed in order to reveal the radio pulsation in 2007. In this Letter, we report the discovery of Delta *g-rays spatially consistent with FIRST J102347.6+003841, at a significance of seven standard deviations, using data obtained by the Fermi Gamma-ray Space Telescope. The Delta *g-ray spectrum can be described by a power law (PL) with a photon index of 2.9 ? 0.2, resulting in an energy flux above 200 MeV of (5.5 ? 0.9) X 10--12 erg cm--2 s--1. The Delta *g-rays likely originate from the MSP PSR J1023+0038, but also possibly from an intrabinary shock between the pulsar and its companion star. To complement the Delta *g-ray study, we also re-investigate the XMM-Newton data taken in 2004 and 2008. Our X-ray spectral analysis suggests that a broken PL with two distinct photon indices describes the X-ray data significantly better than a single PL. This indicates that there exists two components and that both components appear to vary with the orbital phase. The evidence for Delta *g-ray emission conforms with a recent suggestion that Delta *g-rays from PSR J1023+0038 may be responsible for ejecting the disk material out of the system.