Glassy carbon (GC) microelectrodes have been successfully used for detection of electroactive neurotransmitters such as dopamine and serotonin through voltammetry. However, non-electroactive neurotransmitters such as glutamate, lactate, and gamma-aminobutyric acid (GABA) are inherently unsuitable for detection through voltammetry techniques without functionalizing the surface of the microelectrodes. To that end, we present here the immobilization of L-glutamate oxidase (GluOx) enzyme on the surface of GC microelectrodes to enable catalysis of chemical reaction between L-glutamate, oxygen, and water to produce H2O2, an electroactive byproduct that is readily detectable through voltammetry. This immobilization of GluOx on the surface of bare GC microelectrodes and the subsequent catalytic reduction of H2O2 through fast scan cyclic voltammetry (FSCV) helped demonstrate indirect in vitro detection of glutamate, a non-electroactive molecule, at concentrations as low as 10 nM. The functionalized microelectrodes formed part of 4-channel arrays of microelectrodes (30 m x 60 m) on a 1.6 cm long neural probe supported on a flexible polymer, with potential for in vivo applications. The type and strength of the bond between the GC microelectrode surface and its functional groups on one hand, and glutamate and the immobilized functionalization matrix on the other hand, were investigated through molecular dynamics (MD) modeling and Fourier Transform Infrared Spectroscopy (FTIR). Both MD modeling and FTIR demonstrated the presence of several covalent bonds in the form of C-O (carbon-oxygen polar covalent bond), C=O (carbonyl), C-H (alkenyl), N-H (hydrogen bond), C-N (carbon-nitrogen single bond), and C≡N (triple carbon nitrogen bond). Further, penetration tests on agarose hydrogel model confirmed that the probes are mechanically robust with their penetrating forces being much lower than the fracture force of the probe material.