Let (T_n)_n≥0 be the Tribonacci sequence defined by the recurrence T_n+2 = T_n + T_n+1, with T₀ = 0 and T₁ = T₂ = 1. In this short note, we prove that there are no integer solutions (u, m) to the Brocard-Ramanujan equation m! + 1 = u² where u is a Tribonacci number.