MUSE, the Multi Unit Spectroscopic Explorer,1 is an integral-field spectrograph under construction for the ESO VLT to see first light in 2013. It can record spectra of a 1'x1' field on the sky at a sampling of 0''.2x0''.2, over a wavelength range from 4650 to 9300Å. The data reduction for this instrument is the process which converts raw data from the 24 CCDs into a combined datacube (with two spatial and one wavelength axis) which is corrected for instrumental and atmospheric effects. Since the instrument consists of many subunits (24 integral-field units, each slicing the light into 48 parts, i. e. 1152 regions with a total of almost 90000 spectra per exposure), this task requires many steps and is computationally expensive, in terms of processing speed, memory usage, and disk input/output. The data reduction software is designed to be mostly run as an automated pipeline and to fit into the open source environment of the ESO data flow as well as into a data management system based on AstroWISE. We describe the functionality of the pipeline, highlight details of new and unorthodox processing steps, discuss which algorithms and code could be used from other projects. Finally, we show the performance on both laboratory data as well as simulated scientific data.