The ϒ(1S)μ+μ− invariant-mass distribution is investigated for a possible exotic meson state composed of two b quarks and two b¯¯ quarks, Xbb¯bb¯. The analysis is based on a data sample of pp collisions recorded with the LHCb detector at centre-of-mass energies s√=7, 8 and 13 TeV, corresponding to an integrated luminosity of 6.3 fb−1. No significant excess is found, and upper limits are set on the product of the production cross-section and the branching fraction as functions of the mass of the Xbb¯bb¯ state. The limits are set in the fiducial volume where all muons have pseudorapidity in the range [2.0, 5.0], and the Xbb¯bb¯ state has rapidity in the range [2.0, 4.5] and transverse momentum less than 15 GeV/c.