Thirteen years of continuous atmospheric carbon dioxide and methane measurements at the Mauna Loa Observatory in Hawaii are used to determine the methane emission rate from the summit of Mauna Loa volcano. We find no measurable methane emissions coming from the summit area, with a 95% confidence upper limit of 9 t CH4 yr-1. Recent studies have detected 10 ppb CH4 in the Martian atmosphere, requiring emissions of about 300 t CH4 yr-1. Volcanic activity has been suggested as a source of abiogenic CH4 on Mars, either by magmatic degassing or reactions in hydrothermal fluids heated by a magma intrusion. The most recent lava flows on Mars (2 My ago) are on the Tharsis shield volcanoes, which may still be active. If Mauna Loa is a valid terrestrial analog, our findings suggest that volcanic activity is not a significant source of methane to the Martian atmosphere.