HD 72089 is situated behind the Vela supernova remnant, and the interstellar absorption lines in the spectrum of this star are remarkable for two reasons. First, there are six distinct velocity components that span the (heliocentric) velocity range -60 to +121 km s(-1) in the lines of Na I and Ca II. Second, two of the components at high velocity, one at +85 km s(-1) and another at +121.5 km s(-1), have densities that are large enough to produce observable lines from neutral carbon. The gas moving at +121.5 km s(-1) has such a targe pressure that the excited fine-structure levels of the ground electronic state of C I are collisionally populated nearly in proportion to their level degeneracies. This high-velocity gas exhibits unusually low column densities of Mg I and Na I, compared to that of C I. We propose that the +121.5 km s(-1) component represents gas that has cooled and recombined in a zone that follows a shock driven into a cloud by the very recent passage of a supernova blast wave. A representative preshock density of n(H) similar to 13 cm(-3) and velocity nu(s) = 100 km s(-1) is indicated by the strength of diffuse [O III] emission lines seen in directions very near HD 72089. The strong collisional population of excited C I and apparent absence of excited levels of O I give a most favorable fit to the conditions 1000 < n(H) < 2900 cm(-3) over a temperature range 300 < T < 1000 K. The fact that the compression is not substantially more than this indicates that the preshock gas may have had an embedded, transverse magnetic field with a strength B greater than or similar to 1 mu G. The large dynamical pressure of the supernova blast wave that would be needed to create the cloud shock that we describe implies that the energy of the supernova was 8 x 10(51) ergs, if the Vela remnant is 500 pc away. We can bring this value much closer to typical supernova energies E less than or similar to 10(51) ergs if the distance to the remnant is revised downward by at least a factor of 2.