The aim of this study was to investigate the effect of far infrared irradiation (FIR) on nutraceutical compounds, viz. total phenolic content, total flavonoids, and antioxidant capacity, of Angelica gigas Nakai (AGN). The FIR treatment was applied for 30 min with varied temperatures of 120, 140, 160, 180, 200, 220, and 240 °C. Results showed that FIR increased total phenolic and flavonoid content in AGN at 220 °C. The HPLC results revealed higher quantities of decursin (62.48 mg/g) and decursinol angelate (41.51 mg/g) at 220 °C compared to control (38.70 mg/g, 27.54 mg/g, respectively). The antioxidant capacity of AGN was also increased at 220 °C, as measured by 1,1-diphenyl-2-picrylhydrazyl (DPPH), ferric reducing antioxidant power (FRAP), and the phosphomolybdenum (PPMD) method. A further increase of the FIR temperature caused a reduction of compound content. In addition, the results also showed a strong correlation between phenolic content and antioxidant properties of AGN powder. These findings will help to further improve the nutraceutical profile of AGN powder by optimizing the FIR conditions.