If confirmed, the extremely low concentrations of methane (CH4) detected in the Martian atmosphere may represent reservoirs and emission processes that would normally be considered negligible on Earth. One such process is the release of ancient volatiles from fluid inclusions and interstitial sites in rocks and minerals during erosion or geothermal activity. Using a highly sensitive rock-crushing and mass-spectrometry technique previously shown to detect CH4 in serpentinites and hydrothermal mineral deposits, we have demonstrated that CH4 and other ancient volatiles can be recovered from basalt, the dominant rock type on the Martian surface. Basalt samples from a wide range of ages and geological systems were tested, all of which released CH4 when crushed. Oxidative weathering was associated with lower quantities of CH4. Otherwise, CH4 recoverability showed no relationship with age or geological context. Mineral veins, cross-cutting one locality were found to share the volatile composition of the basalt. In general, the results suggest that CH4-release from ancient basalts could be a significant process on Mars, which could be further investigated by Martian rovers using a similar rock-crushing and mass spectrometry technique in situ.