We report the detection of far-IR CO rotational emission from the prototypical Seyfert 2 galaxy NGC 1068. Using Herschel-PACS, we have detected 11 transitions in the J_(upper) = 14-30 (E_(upper)/k_B = 580-2565 K) range, all of which are consistent with arising from within the central 10" (700 pc). The detected transitions are modeled as arising from two different components: a moderate-excitation (ME) component close to the galaxy systemic velocity and a high-excitation (HE) component that is blueshifted by ~80 km s^(–1). We employ a large velocity gradient model and derive n_(H2) ~ 10^(5.6) cm^(–3), T_(kin) ~ 170 K, and M_(H2) ~ 10^(6.7) M_☉ for the ME component and n_(H2) ~ 10^(6.4) cm^(–3), T_(kin) ~ 570 K, and M_(H2) ~ 10^(5.6) M_☉ for the HE component, although for both components the uncertainties in the density and mass are ±(0.6-0.9) dex. Both components arise from denser and possibly warmer gas than traced by low-J CO transitions, and the ME component likely makes a significant contribution to the mass budget in the nuclear region. We compare the CO line profiles with those of other molecular tracers observed at higher spatial and spectral resolution and find that the ME transitions are consistent with these lines arising in the ~200 pc diameter ring of material traced by H_2 1-0 S(1) observations. The blueshift of the HE lines may also be consistent with the bluest regions of this H_2 ring, but a better kinematic match is found with a clump of infalling gas ~40 pc north of the active galactic nucleus (AGN). We consider potential heating mechanisms and conclude that X-ray- or shock heating of both components is viable, while far-UV heating is unlikely. We discuss the prospects of placing the HE component near the AGN and conclude that while the moderate thermal pressure precludes an association with the ~1 pc radius H_2O maser disk, the HE component could potentially be located only a few parsecs more distant from the AGN and might then provide the N_H ~ 10^(25) cm^(–2) column obscuring the nuclear hard X-rays. Finally, we also report sensitive upper limits extending up to J_(upper) = 50, which place constraints on a previous model prediction for the CO emission from the X-ray obscuring torus.