  The Kratzer's potential $V(r)=g_{1}/r^{2}-g_{2}/r$ is studied in quantum
mechanics with a generalized uncertainty principle, which includes a minimal
length $\left( \Delta X\right) _{\min}=\hbar\sqrt{5\beta}$. In momentum
representation, the Schr\"{o}dinger equation is a generalized Heun's
differential equation, which reduces to a hypergeometric and to a Heun's
equations in special cases. We explicitly show that the presence of this finite
length regularizes the potential in the range of the coupling constant $g_{1}$
where the corresponding Hamiltonian is not self-adjoint. In coordinate space,
we perturbatively derive an analytical expression for the bound states spectrum
in the first order of the deformation parameter $\beta$. We qualitatively
discuss the effect of the minimal length on the vibration-rotation energy
levels of diatomic molecules, through the Kratzer interaction. By comparison
with an experimental result of the hydrogen molecule, an upper bound for the
minimal length is found to be of about $0.01$ \AA . We argue that the minimal
length would have some physical importance in studying the spectra of such
systems
