We demonstrate, for the first time to our knowledge, the generation of squeezed light by means of soliton self-phase modulation in microstructure fiber. We observe and characterize the formation of solitons in the microstructure fiber at 1550 nm. A maximum squeezing of 2.7 dB is observed, corresponding to 4.0 dB after correcting for detection losses. The dependence of this quantum-noise reduction on various system parameters is studied in detail. Features of the microstructure fiber can be exploited for generation of low-energy continuous-variable entangled pulses for use in all-fiber teleportation experiments.