We measure hyperfine structure in the metastable 3 P 2 state of 173 Yb and extract the nuclear magnetic octupole moment. We populate the state using dipole-allowed transitions through the 3 P 1 and 3 S1 states. We measure frequencies of hyperfine transitions of the 3 P 2 → 3 S1 line at 770 nm using a Rb-stabilized ring cavity resonator with a precision of 200 kHz. Second-order corrections due to perturbations from the nearby 3 P 1 and 1 P 1 states are below 30 kHz. We obtain the hyperfine coefficients as: A = −742.11(2) MHz, B = 1339.2(2) MHz, which represent two orders-of-magnitude improvement in precision, and C = 0.54(2) MHz. From atomic structure calculations, we obtain the nuclear moments: quadrupole Q = 2.46(12) b and octupole Ω = −34.4(21) b ×µN .