A robust strain sensor is demonstrated based on a microfiber Mach-Zehnder interferometer (MMZI) encapsulated by the polymer polydimethylsiloxane (PDMS). Benefiting from the low Young's modulus of PDMS, both a robust structure and high sensitivity can be realized based on three different encapsulations. In the experiment, the proposed sensors are fabricated and tested with strain sensitivities ranging from -20.95 pm/με to 127.00 pm/με within the wavelength range of 1200-1650 nm. Compared with the bare MMZI sensor, at least one order of magnitude higher sensitivity is reached. To further evaluate the performance of the sensor, the dependences of sensitivity on probing wavelength and the different types and quantities of polymers used in encapsulation are discussed. Results show that the sensitivity of the sensor will increase with the probing wavelength. The type and quantity of polymer used are also very critical to sensitivity. Additionally, a response time of 24.72 ms can be reached. Good recoverability and repeatability of the sensor are also demonstrated by repeated experiments. The strain sensor demonstrated here shows the advantages of simple fabrication, robust structure, high and tunable sensitivity, fast response, good recoverability and repeatability.