The Gemini Planet Imager (GPI) is a new facility instrument for the Gemini Observatory designed to provide direct detection and characterization of planets and debris disks around stars in the solar neighborhood. In addition to its extreme adaptive optics and coronagraphic systems which give access to high angular resolution and high-contrast imaging capabilities, GPI contains an integral field spectrograph providing low resolution spectroscopy across five bands between 0.95 and 2.5 μm. This paper describes the sequence of processing steps required for the spectro-photometric calibration of GPI science data, and the necessary calibration files. Based on calibration observations of the white dwarf HD 8049 B we estimate that the systematic error in spectra extracted from GPI observations is less than 5%. The flux ratio of the occulted star and fiducial satellite spots within coronagraphic GPI observations, required to estimate the magnitude difference between a target and any resolved companions, was measured in the H-band to be μm = 9.23 ± 0.06 in laboratory measurements and μm = 9.39 ± 0.11 using on-sky observations. Laboratory measurements for the Y, J, K1 and K2 filters are also presented. The total throughput of GPI, Gemini South and the atmosphere of the Earth was also measured in each photometric passband, with a typical throughput in H-band of 18% in the non-coronagraphic mode, with some variation observed over the six-month period for which observations were available. We also report ongoing development and improvement of the data cube extraction algorithm.