Natural deep eutectic solvents (NADES) are a type of ionic liquid (IL) or deep eutectic solvent (DES), the ingredients of which are exclusively natural products (non-toxic and environmentally friendly). Here, we explore the potential of NADES as an alternative to conventional organic solvents (e.g., aqueous methanol or ethanol) for the extraction of flavonoids from Scutellaria baicalensis stem bark to investigate their extractability depending on structural variation. Four NADES, each containing citric acid in combination with β-alanine, glucose, xylitol, or proline (at a molar ratio of 1:1), and a variable amount of water, were used to extract the flavonoid aglycones: baicalein (1), scutellarein (3), wogonin (5), and oroxylin A (7), and their glycosides, baicalin (2), scutellarin (4), wogonoside (6) and oroxyloside (8) from the powdered bark of S. baicalensis. The chemical profile and yield of the extracts were determined using HPTLC and HPLC. The extractability of individual flavonoids was found to be influenced by the concentration of water (20–60%, w/w) in the NADES. Among the tested flavonoids, the extraction yield of baicalein (1), scutellarein (3), wogonin (5), oroxylin A (7) with NADES was 2 to 6 times that of aqueous methanol. However, the amount of their corresponding glycosides (baicalin (2), wogonoside (6) and oroxyloside (8)) extracted with NADES was only 1.5–1.8 times higher than with aqueous methanol. Interestingly, the more hydrophilic glycosides were less extracted than their corresponding aglycones despite the high hydrophilicity of the NADES. These results prove that NADES may be used for extraction of compounds with a wide range of hydrophilicity.