The photometric calibration of the Sloan Digital Sky Survey (SDSS) is a multi-step process which involves data from three different telescopes: the 1.0-m telescope at the US Naval Observatory (USNO), Flagstaff Station, Arizona (which was used to establish the SDSS standard star network); the SDSS 0.5-m Photometric Telescope (PT) at the Apache Point Observatory (APO), New Mexico (which calculates nightly extinctions and calibrates secondary patch transfer fields); and the SDSS 2.5-m telescope at APO (which obtains the imaging data for the SDSS proper). In this paper, we describe the Monitor Telescope Pipeline, MTPIPE, the software pipeline used in processing the data from the single-CCD telescopes used in the photometric calibration of the SDSS (i.e., the USNO 1.0-m and the PT). We also describe transformation equations that convert photometry on the USNO-1.0m u'g'r'i'z' system to photometry the SDSS 2.5m ugriz system and the results of various validation tests of the MTPIPE software. Further, we discuss the semi-automated PT factory, which runs MTPIPE in the day-to-day standard SDSS operations at Fermilab. Finally, we discuss the use of MTPIPE in current SDSS-related projects, including the Southern u'g'r'i'z' Standard Star project, the u'g'r'i'z' Open Star Clusters project, and the SDSS extension (SDSS-II). ; Comment: 24 pages, 16 figures (1 color), accepted for publication in Astronomische Nachrichten