We report the observation of the hyperfine spectrum of the weak P(63) 4-4 line of the B − X electronic transition of molecular iodine 127I2 near 652.4 nm, using frequency-modulated saturated absorption spectroscopy. Through the precise measurements of the absolute frequencies of hyperfine components, we estimate electric quadrupole and magnetic spin-rotation constants. Additionally, we determine the center of gravity of the P(63) transition of the 4-4 vibrational band, resulting in a 250-fold improvement in the precision of its position. We also note an interesting overlap of the hyperfine transitions of the P(63)4-4 line with the UV 1S0–3P1 narrow intercombination transition of cadmium atoms, which occurs near the second harmonic of the master laser radiation, corresponding to 326.2 nm. This study contributes to updating the iodine atlas, improving the precision of the empirical formulae, and providing an important frequency reference for precision spectroscopy of the narrow intercombination transition of atomic cadmium.