The first measurement of the production rate of Ξb- baryons in pp collisions relative to that of Λb0 baryons is reported, using data samples collected by the LHCb experiment, and corresponding to integrated luminosities of 1, 2 and 1.6 fb-1 at s=7, 8 and 13 TeV, respectively. In the kinematic region 2<η<6 and pT<20 GeV/c, we measure fΞb-fΛb0B(Ξb-→J/ψΞ-)B(Λb0→J/ψΛ)=(10.8±0.9±0.8)×10-2 [s=7,8 TeV], fΞb-fΛb0B(Ξb-→J/ψΞ-)B(Λb0→J/ψΛ)=(13.1±1.1±1.0)×10-2 [s=13 TeV], where fΞb- and fΛb0 are the fragmentation fractions of b quarks into Ξb- and Λb0 baryons, respectively; B represents branching fractions; and the uncertainties are due to statistical and experimental systematic sources. The values of fΞb-/fΛb0 are obtained by invoking SU(3) symmetry in the Ξb-→J/ψΞ- and Λb0→J/ψΛ decays. Production asymmetries between Ξb- and Ξb+ baryons are also reported. The mass of the Ξb- baryon is also measured relative to that of the Λb0 baryon, from which it is found that m(Ξb-)=5796.70±0.39±0.15±0.17 MeV/c2, where the last uncertainty is due to the precision on the known Λb0 mass. This result represents the most precise determination of the Ξb- mass.