Mapping Nearby Galaxies at Apache Point Observatory ( MaNGA ) is an optical fiber-bundle integral-field unit ( IFU ) spectroscopic survey that is one of three core programs in the fourth-generation Sloan Digital Sky Survey ( SDSS-IV ) . With a spectral coverage of 3622 – 10,354 Ã Â and an average footprint of \sim 500 arcsec ^ { 2 } per IFU the scientific data products derived from MaNGA will permit exploration of the internal structure of a statistically large sample of 10,000 low redshift galaxies in unprecedented detail . Comprising 174 individually pluggable science and calibration IFUs with a near-constant data stream , MaNGA is expected to obtain \sim 100 million raw-frame spectra and \sim 10 million reduced galaxy spectra over the six-year lifetime of the survey . In this contribution , we describe the MaNGA Data Reduction Pipeline ( DRP ) algorithms and centralized metadata framework that produces sky-subtracted , spectrophotometrically calibrated spectra and rectified 3-D data cubes that combine individual dithered observations . For the 1390 galaxy data cubes released in Summer 2016 as part of SDSS-IV Data Release 13 ( DR13 ) , we demonstrate that the MaNGA data have nearly Poisson-limited sky subtraction shortward of \sim 8500 Ã Â and reach a typical 10 \sigma limiting continuum surface brightness \mu = 23.5 AB arcsec ^ { -2 } in a five arcsec diameter aperture in the g band . The wavelength calibration of the MaNGA data is accurate to 5 km s ^ { -1 } Â rms , with a median spatial resolution of 2.54 arcsec FWHM ( 1.8 kpc at the median redshift of 0.037 ) and a median spectral resolution of \sigma = 72 km s ^ { -1 } .