We investigate the multiplicity properties of 408 B-type stars observed in the 30 Doradus region of the Large Magellanic Cloud with multi-epoch spectroscopy from the VLT-FLAMES Tarantula Survey (VFTS). We use a cross-correlation method to estimate relative radial velocities from the helium and metal absorption lines for each of our targets. Objects with significant radial-velocity variations (and with an amplitude larger than 16 km s-1) are classified as spectroscopic binaries. We find an observed spectroscopic binary fraction (defined by periods of <103.5 d and mass ratios >0.1) for the B-type stars, fB(obs) = 0.25 ± 0.02, which appears constant across the field of view, except for the two older clusters (Hodge 301 and SL 639). These two clusters have significantly lower binary fractions of 0.08 ± 0.08 and 0.10 ± 0.09, respectively. Using synthetic populations and a model of our observed epochs and their potential biases, we constrain the intrinsic multiplicity properties of the dwarf and giant (i.e. relatively unevolved) B-type stars in 30 Dor. We obtain a present-day binary fraction fB(true) = 0.58 ± 0.11, with a flat period distribution. Within the uncertainties, the multiplicity properties of the B-type stars agree with those for the O stars in 30 Dor from the VFTS. Appendices A, B are available in electronic form at http://www.aanda.orgFull Tables 2 and 3 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/580/A93