A device to measure a fluid pressure comprises a pressure sensing element 10 and a pressure readout element 20. The pressure sensing element 10 comprises a cavity 11 capped by a flexible membrane 13, the cavity having a length d that varies with the fluid pressure P1 applied on the flexible membrane 13. The pressure readout element 20 comprises a light source 24 for providing an incident beam of a determined wavelength range directed towards the cavity and an optical spectral analyzer 25 for measuring a power spectrum of a return beam reflected by the cavity, and processing means 27 for determining the cavity length d and the fluid pressure P1 based on the power spectrum.