Here, we developed functional nucleic acid (FNA)-encapsulated electrospun fibermats. To facilitate stable FNA encapsulation in the γ-PGA/GPTMS fibermats, we used the FNA as an FNA/streptavidin complex, and as a representative FNA, we selected a DNAzyme, the DNA/hemin complex, which is composed of G-quadraplex-forming single-stranded DNA and hemin and exhibits oxidation activity with the aid of a cocatalyst, H2O2. Scanning electron microscopy and Fourier-transform infrared spectroscopy measurements revealed that encapsulation of the DNA/hemin complex (∼1 wt % against the γ-PGA/GPTMS hybrid) in the nanofibers of the γ-PGA/GPTMS fibermats did not affect the structure of the original nanofibers. However, because a unique MW-dependent molecular permeability originated from the 3D network structure of the γ-PGA/GPTMS hybrid, low-MW substrates such as 4-aminoantipyrine, N-ethyl-N-(2-hydroxy-3-sulfopropyl)-3-methylaniline, and luminol were able to reach the encapsulated DNA/hemin complex by permeating to the inside of the nanofibers from an immersion buffer and then underwent catalytic oxidation. Conversely, nucleases, which are proteins featuring high MWs (>5 kDa), could not penetrate the γ-PGA/GPTMS nanofibers, and the encapsulated DNA/hemin complex was therefore effectively protected against nuclease digestion. Thus, encapsulating FNAs on the inside of the nanofibers of fibermats offers clear advantages for the practical application of FNAs in sensors and drugs, particularly for use in the in vivo circumstances.