The first phase of the Carnegie Supernova Project (CSP-I) was a dedicated supernova follow-up program based at the Las Campanas Observatory that collected science data of young, low-redshift supernovae between 2004 and 2009. Presented in this paper is the CSP-I photometric data release of low-redshift stripped-envelope core-collapse supernovae. The data consist of optical (uBgV ri) photometry of 34 objects, with a subset of 26 having near-infrared (YJH) photometry. Twenty objects have optical pre-maximum coverage with a subset of 12 beginning at least five days prior to the epoch of B-band maximum brightness. In the near-infrared, 17 objects have pre-maximum observations with a subset of 14 beginning at least five days prior to the epoch of J-band maximum brightness. Analysis of this photometric data release is presented in companion papers focusing on techniques to estimate host-galaxy extinction (Stritzinger et al., submitted) and the light-curve and progenitor star properties of the sample (Taddia et al., submitted). The analysis of an accompanying visual-wavelength spectroscopy sample of ~150 spectra will be the subject of a future paper.