Abstract Absorption spectroscopy is a fundamental tool for probing molecular structure1. However, performing absorption spectroscopy on individual molecules is challenging because of the low signal-to-noise ratio2,3. Here we report on non-destructive absorption spectroscopy on a mid-infrared vibrational transition in a single molecular ion that is co-trapped with an atomic ion. The absorption of a single photon is detected by the momentum transfer from the absorbed photon onto the molecule.