Optical fiber interferometry holds many advantages for the online measurement of high-precision surfaces. Here, a fiber interferometer with a wavelength-scanning probe is reported. Such an interferometer requires active stabilization against the effects of temperature drift and vibration. A method of multiplexing dual wavelengths into the same fiber, combined with rapid phase shifting and real-time phase calculation, is investigated. Experimental data show the successful stabilization of the interferometer regardless of environmental perturbation.