Conventional pressure sensors rely on diaphragms with large surface areas, which deform in response to pressure. Down scalability of these devices is one of the major challenges of the technology along with reducing the overall actuation voltage and achieving ultra-high sensitivity. We present a sensitive miniature pressure sensor based on the change in the physisorbed gases with the pressure of the surrounding air. The sensor consists of a suspended individual multiwall carbon nanotube (MWCNT) clamped on Au electrodes by electron-beam-induced deposition (EBID) of Pt. The variation in the surrounding pressure is shown to be tracked by monitoring the change in the resistivity, hence resistance, of the MWCNT bridge structure due to the change in percentage of oxygen and humidity in the surrounding medium with pressure. The experimental data reveal the practicability and simplicity of the proposed pressure sensor.