This Letter describes a measurement of the muon cross section originating from b-quark decay in the forward rapidity range 2.4<| y(&mgr;)|<3.2 in p&pmacr; collisions at sqrt[s] = 1.8 TeV. The data used in this analysis were collected by the D0 experiment at the Fermilab Tevatron. We find that next-to-leading-order QCD calculations underestimate b-quark production by a factor of 4 in the forward rapidity region.