The authors demonstrate a microfibre Mach–Zehnder interferometer (MMZI) using a single silica optical microfibre fabricated using flame-heated-drawing technique. The microfibre was cut into two parts: the first part is stretched straight, whereas the second part is bent and manipulated to form an MMZI. The fabricated MMZI shows good interference fringes with the highest extinction ratio of 14 dB. The free spectral range (FSR) of the interferometer can be tuned from 0.14 to 0.75 nm by micromanipulating the path-length difference of the MMZI under an optical microscope. It is also observed that the FSR is unaffected by the volatility of the surrounding air. The MMZI is also used to demonstrate a compact current sensor. The proposed sensor uses a copper wire, which touching one arm of the MMZI so that the wavelength shift is linearly proportional to the square of the amount of the flowing current. The slope efficiency of the sensor is obtained at 60.17 pm/A2.