A search for the doubly heavy Ξ0bc baryon using its decay to the D0pK– final state is performed using proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the LHCb experiment between 2016 and 2018, corresponding to an integrated luminosity of 5.4 fb−1. No significant signal is found in the invariant mass range from 6.7 to 7.2 GeV/c2. Upper limits are set at 95% credibility level on the ratio of the Ξ0bc production cross-section times its branching fraction to D0pK− relative to that of the Λ0b→D0pK− decay. The limits are set as a function of the Ξ0bc mass and lifetime hypotheses, in the rapidity range from 2.0 to 4.5 and in the transverse momentum region from 5 to 25 GeV/c. Upper limits range from 1.7 × 10−2 to 3.0 × 10−1 for the considered Ξ0bc mass and lifetime hypotheses.