We have detected the CO(6-5), CO(7-6), and [C I] 370 μm lines from the nuclear region of NGC 891 with our submillimeter grating spectrometer ZEUS on the Caltech Submillimeter Observatory. These lines provide constraints on photodissociation region (PDR) and shock models that have been invoked to explain the H₂ S(0), S(1), and S(2) lines observed with Spitzer. We analyze our data together with the H₂ lines, CO(3-2), and infrared continuum from the literature using a combined PDR/shock model. We find that the mid-J CO originates almost entirely from shock-excited warm molecular gas; contributions from PDRs are negligible. Also, almost all of the H₂ S(2) line and half of the S(1) line are predicted to emerge from shocks. Shocks with a pre-shock density of 2 × 10⁴ cm^–3 and velocities of 10 km s^–1 and 20 km s^–1 for C-shocks and J-shocks, respectively, provide the best fit. In contrast, the [C I] line emission arises exclusively from the PDR component, which is best parameterized by a density of 3.2 × 10³ cm^–3 and a far-ultraviolet field of G_o = 100 for both PDR/shock-type combinations. Our mid-J CO observations show that turbulence is a very important heating source in molecular clouds, even in normal quiescent galaxies. The most likely energy sources for the shocks are supernovae or outflows from young stellar objects. The energetics of these shock sources favor C-shock excitation of the lines.