We report the first detection of high-energy X-ray ( E > 10 keV ) emission from the Galactic Center non-thermal filament G359.89 - 0.08 ( Sgr A - E ) using data acquired with the Nuclear Spectroscopic Telescope Array ( NuSTAR ) . The bright filament was detected up to \sim 50 keV during a NuSTAR Galactic Center monitoring campaign . The featureless power-law spectrum with a photon index \Gamma \approx 2.3 confirms a non-thermal emission mechanism . The observed flux in the 3 - 79 keV band is F _ { X } = ( 2.0 \pm 0.1 ) \times 10 ^ { -12 } erg cm ^ { -2 } s ^ { -1 } , corresponding to an unabsorbed X-ray luminosity L _ { X } = ( 2.6 \pm 0.8 ) \times 10 ^ { 34 } erg s ^ { -1 } assuming a distance of 8.0 kpc . Based on theoretical predictions and observations , we conclude that Sgr A - E is unlikely to be a pulsar wind nebula ( PWN ) or supernova remnant - molecular cloud ( SNR - MC ) interaction , as previously hypothesized . Instead , the emission could be due to a magnetic flux tube which traps TeV electrons . We propose two possible TeV electron sources : old PWNe ( up to \sim 100 kyr ) with low surface brightness and radii up to \sim 30 pc or molecular clouds ( MCs ) illuminated by cosmic rays ( CRs ) from CR accelerators such as SNRs or Sgr A* .