Spectrally resolved photoacoustic imaging is promising for label-free imaging in optically scattering materials. However, this technique often requires acquisition of a separate image at each wavelength of interest. This reduces imaging speeds and causes errors if the sample changes in time between images acquired at different wavelengths. We demonstrate a solution to this problem by using dual-comb spectroscopy for photoacoustic measurements. This approach enables a photoacoustic measurement at thousands of wavelengths simultaneously. In this technique, two optical-frequency combs are interfered on a sample and the resulting pressure wave is measured with an ultrasound transducer. This acoustic signal is processed in the frequency-domain to obtain an optical absorption spectrum. For a proof-of-concept demonstration, we measure photoacoustic signals from polymer films. The absorption spectra obtained from these measurements agree with those measured using a spectrophotometer. Improving the signal-to-noise ratio of the dual-comb photoacoustic spectrometer could enable high-speed spectrally resolved photoacoustic imaging.