We report the results of a search for the decay B0 → X(3872)(→ J/ψ π+ π−)γ. The analysis is performed on a data sample corresponding to an integrated luminosity of 711 fb^−1 and containing 772 × 10^6 BB ̄ pairs, collected with the Belle detector at the KEKB asymmetric-energy e+e- collider running at the Υ(4S) resonance energy. We find no evidence for a signal and place an upper limit of B(B0 → X(3872) γ) × B(X(3872) → J/ψ π+ π−) < 5.1 × 10^−7 at 90% confidence level.