One of the main goals of the HERA-B experiment at DESY in Hamburg, Germany, is to study the properties of B-mesons with the emphasis on CP violation. B-mesons are produced in hadronic interactions of a 920-GeV proton beam with an internal wire target. An effective bunch crossing rate of about 8.5 MHz leads to about 200 charged tracks per event. Therefore, a highly selective and efficient trigger system providing high suppression of background events is required. The HERA-B trigger system consists of four levels. A rate reduction factor of 200 is aimed at by the first-level trigger (FLT). The muon pretrigger system, as a part of the FLT, is a modular system consisting of about 100 large-size VME modules of three different types: the pretrigger link board (PLB), the pretrigger coincidence unit (PCU), and the pretrigger message generator (PMG). The data rate processed by the pretrigger system is about 19.5 GByte/s. The PLBs process digitized hit information in eight independent electronic channels in parallel. Every electronic channel handles 32 bits of hit information received from the front-end driver buffer system. Optical links operating at 800 Mb/s transmit the data after serialization to PCUs, which calculate coincidences using complex programmable logic devices. The PMGs transform this coincidence information into messages for the FLT processors. The concept and design as well as results of the muon pretrigger running at HERA-B are presented.