Doppler asymmetric spatial heterodyne spectroscopy (DASH) technique has developed rapidly in passive Doppler-shift measurements of atmospheric emission lines over the last decade. With the advantages of high phase shift sensitivity, compact, and rugged structure, DASH is proposed to be used for celestial autonomous navigation based on Doppler radial velocity measurement in this work. Unlike atmospheric emission lines, almost all targeted lines in the research field of deep-space exploration are the absorption lines of stars, so a mathematical model for the Doppler-shift measurements of absorption lines with a DASH interferometer is established. According to the analysis of the components of the interferogram received by the detector array, we find that the interferogram generated only by absorption lines in a passband can be extracted and processed by a method similar to the approach to studying the emission lines. In the end, numerical simulation experiments of Doppler-shift measurements of absorption lines are carried out. The simulation results show that the relative errors of the retrieved speeds are less than 0.7% under ideal conditions, proving the feasibility of measuring Doppler shifts of absorption lines by DASH instruments. © 2020 Chinese Physical Society and IOP Publishing Ltd.