A search for baryon-number-violating $Xi_b^0$ oscillations is performed with a sample of $pp$ collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of 3 fb$^{-1}$. The baryon number at the moment of production is identified by requiring that the $Xi_b^0$ come from the decay of a resonance $Xi_b^{*-} to Xi_b^0 pi^-$ or $Xi_b^{prime-} to Xi_b^0 pi^-$, and the baryon number at the moment of decay is identified from the final state using the decays $Xi_b^0 to Xi_c^+ pi^-, ~ Xi_c^+ to p K^- pi^+$. No evidence of baryon number violation is found, and an upper limit at the 95% confidence level is set on the oscillation rate of $omega < 0.08$ ps$^{-1}$, where $omega$ is the associated angular frequency.
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