In this paper, a novel MEMS Mach-Zehnder interferometer optical switch is presented. Switching is achieved by tuning the vertical gap between two coupled waveguides through the application of a reverse bias on a p-i-n junction. The switching requires a voltage as low as 4.4V and provides an extinction ratio above 15dB within a 34 nm bandwidth in the C-band. The device also serves as a very efficient optical phase modulator, being able to modify the optical phase by more than 4π with only 6.5V voltage in a 140μm-long waveguide. Our work provides a solution to on-chip optical switching for low-voltage applications. The switch is fabricated on an indium-phosphide membrane on a silicon substrate, which enables the integration with active components (e.g. amplifiers, lasers, detectors) on a single chip.