The subject of this thesis is the development and characterization of one of the timing sub-systems in the Mu3e experiment - namely the Scintillating Fiber detector. Prototypes of staggered scintillating fibers with a diameter of 250 um are constructed in two distinct readout configurations within the scope of the present work. Silicon photomultipliers with different geometries are further explored for the optical readout of the fibers. The prototypes are then characterized in accelerated proton and electron beams, as well as with radioactive strontium sources. To evaluate their performance, the author developed dedicated data acquisition systems featuring established instruments for nuclear physics experiments and novel digitizing electronics. Following a comprehensive analysis, a time resolution better than 280 ps and an efficiency above 95 % are measured with the produced scintillating fiber ribbons. As a result, their feasibility for the Mu3e experiment is proven. The design of the fiber detector is refined based on the observed results and the experience gained in handling and producing these prototypes.