We report a measurement of the fraction of b quarks produced diffractively in &pmacr;p collisions at sqrt[s] = 1.8 TeV. Diffraction is identified by the absence of particles in a forward pseudorapidity region. From events with an electron of transverse momentum 9.5<p(e)(T)<20 GeV/ c within the pseudorapidity region |eta|<1.1, the ratio of diffractive to total b-quark production rates is found to be R(&bmacr;b) = [0.62+/-0.19(stat)+/-0.16(syst)]%. This result is comparable in magnitude to corresponding ratios for W and dijet production but significantly lower than expectations based on factorization.