© 2014, Pleiades Publishing, Ltd. An expression governing Fisher information of vibrational states of a diatomic molecule is obtained in the first-order Wentzel-Kramers-Brillouin (WKB) approximation, and a quantitative criterion of its applicability is proposed. The expression is determined only by the dependence of energy of vibrational levels on quantum number v and the reduced mass of the molecule; it is not related to any additional model assumptions and does not require knowledge of vibrational wavefunction. It is established that the dependence of Fisher information on v attains maximum at certain value v0. The efficiency of the obtained expression is demonstrated by calculating the Fisher information of vibrational levels v = 0–40 of the X1Σg + state of the 7Li2 molecule. It is established that v0 = 23 for this electronic state. Calculation of the Fisher information of levels v = 0–38 of this state with the help of the obtained relation is in excellent (within mean-square deviation σ̄ = 0.01%) agreemen