Sensors that measure dissolved gases directly are needed for environmental, industrial, and biomedical applications. Here we present a hollow core fiber optic sensor capable of measuring dissolved methane gas in liquids using only nanoliters of sample gas. The sensor is based on an anti-resonant hollow core fiber combined with a permeable capillary membrane inlet that extracts gas from the liquid for analysis. Using a small capillary inlet for gas extraction is only possible due to the small amount of sample gas needed for analysis, and it presents new possibilities for dissolved gas analysis in a simple, robust, and compact sensor configuration. We demonstrate the sensing technique using wavelength modulation spectroscopy and measure methane dissolved in water with a 1σ lower detection limit of 230 ppb, a resolution of 45 ppb, and a response time of ∼8min.