Photoionization of excited states of the xenon dimer (${\mathrm{Xe}}_{2}$) has been observed and absolute ionization cross sections have been measured for several laser wavelengths between 248 and 351 nm. Production of the excimers is accomplished by two-photon ionization of ground-state Xe atoms at 193 nm, followed by formation and the subsequent dissociative recombination of $\mathrm{Xe}_{2}^{}{}_{}{}^{+}$ $1{(\frac{1}{2})}_{u}$ ions, collisional and radiative relaxation of the Xe $6p$ and $6{s}^{\ensuremath{'}}$ manifolds, and formation of low-lying excimer states by three-body collisions. Absolute photoionization cross sections are subsequently determined at 351.1, 337.1, 307.9, 277.0, and 248.4 nm by combining a second rare-gas---halide excimer (or ${\mathrm{N}}_{2}$) laser pulse with a microwave-absorption technique to monitor the absolute photoelectron density (in real time) as a function of the intensity of the second laser pulse. The use of microwave absorption allows for the detection of photoelectrons in the presence of a high-pressure background gas. Laser-induced fluorescence and spontaneous emission studies of the temporal behavior of the populations of all of the Xe $6p$ states as well as the $6{s}^{\ensuremath{'}}{(\frac{1}{2})}_{0}$ and $6s{(\frac{3}{2})}_{1}$ levels confirm that a molecule is being photoionized. The molecular states involved are ${0}_{u}^{+},{1}_{g}$, and ${2}_{g}$ which correlate with the $6s{(\frac{3}{2})}_{1}$ excited level and a $^{1}S_{0}$ (ground-state) atom. The optical transitions associated with each laser wavelength $\ensuremath{\lambda}$ studied appear to be ${\mathrm{Xe}}_{2}^{*}{0}_{u}^{+}\ensuremath{\rightarrow}{\mathrm{Xe}}_{2}^{+} 1{(\frac{3}{2})}_{g} (\ensuremath{\lambda}=248.4 \mathrm{nm})$; ${1}_{g} (or {2}_{g})\ensuremath{\rightarrow}1{(\frac{3}{2})}_{u} (\ensuremath{\lambda}=277.0 \mathrm{nm})$; and ${1}_{g} (or {2}_{g})\ensuremath{\rightarrow}1{(\frac{1}{2})}_{u}$ for $\ensuremath{\lambda}=307.9,337.1, \mathrm{and} 351.1$ nm. The discrepancy between the measured cross sections and the values calculated previously (Lorents, Eckstrom, and Huestis, 1973) from a quantum-defect approach is roughly a factor of 2 at 308 nm but increases rapidly at shorter wavelengths. Also, in contrast to theoretical predictions for the $6s$ atomic Xe excited states in which the photoionization cross section $\ensuremath{\sigma}$ falls monotonically with photon energy, the measured $\ensuremath{\sigma}$ peaks at 7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}18}$ ${\mathrm{cm}}^{2}$ for $\ensuremath{\lambda}=308$ nm ($\ensuremath{\hbar}\ensuremath{\omega}=4$ eV). The profile of the photoionization cross-section spectrum that is reported here for $\mathrm{Xe}_{2}^{}{}_{}{}^{*}$ is, however, remarkably similar to that calculated by Rescigno et al. [J. Chem. Phys. 68, 5283 (1978)] for the $^{1}\ensuremath{\Sigma}$ excited state of the ${\mathrm{Ar}}_{2}$ excimer ($\mathrm{Ar}_{2}^{}{}_{}{}^{*}$).