Celestial holography is the conjecture that scattering amplitudes in (d + 2)-dimensional asymptotically Minkowski spacetimes are dual to correlators of a d-dimensional conformal field theory (CFT) on the celestial sphere, called the celestial CFT (CCFT). In a CFT, we can calculate sub-region entanglement Rényi entropies (EREs), including entanglement entropy (EE), from correlators of twist operators, via the replica trick. We argue that CCFT twist operators are holographically dual to cosmic branes in the (d +2)-dimensional spacetime, and that their correlators are holographically dual to the (d +2)-dimensional partition function (the vacuum-to-vacuum scattering amplitude) in the presence of these cosmic branes. We hence compute the EREs of a spherical sub-region of the CCFT’s conformal vacuum, finding the form dictated by conformal symmetry, including a universal contribution determined by the CCFT’s sphere partition function (odd d) or Weyl anomaly (even d). We find that this universal contribution vanishes when d = 4 mod 4, and otherwise is proportional to i times the d^th power of the (d + 2)-dimensional long-distance cutoff in Planck units.