We have developed a theory of optical absorption in quantum-well wires made from indirect-gap semiconductors, such as Si/Si1-xGex, in which the final state is the 1s excitonic state in the lowest conduction subband. The momentum conservation is due to phonons. It is found that the absorption spectra reproduce the density-of-states function for one-dimensional systems, i.e., show a singularity at threshold in the ideal case. Calculations using a Lorentzian broadening indicate that the peak absorption is larger than the constant absorption in quantum wells and the ratio is enhanced when the wire size is about 10 A. © 1993 The American Physical Society.