In this paper, a photometric catalog is presented of V and I photometry of galaxies in the central regions of the Fornax galaxy cluster. Our 11 CCD fields cover 0.17 square degrees in total. The limiting surface brightness is around 24mag/arcsec^2^, similar to that of Ferguson's (1989, Cat. <VII/180>) catalog, whereas our limiting total magnitude is around V=22mag, about two magnitudes fainter. The photometric properties of more than 870 objects are presented as a catalog (Appendix A). The properties and fit parameters of the surface brightness profiles for a sub-sample are presented in a second catalog (Appendix B). Four new dwarf galaxies are added to Ferguson's catalog. However, we confirm that the dwarf galaxies in Fornax follow a similar surface brightness -- magnitude relation as the Local Group dwarfs. They also follow the color (metallicity) -- magnitude relation seen in other galaxy clusters. A formerly suspected excess of dwarf galaxies surrounding the central giant cD galaxy NGC 1399 can be explained by the superposition of a background cluster at z=0.11 (Hilker et al. 1998, Cat. <J/A+AS/134/75>, Paper II in this series).