This paper aims to establish a Berry-Esseen-like theorem for Markov processes conditioned not to be absorbed. That is the Kolmogorov distance between the conditional distribution of the renormalized centered empirical mean and a Gaussian law decays as 1/ $\sqrt{t}$. The main assumption is that a given Doob h-transform of the sub-Markovian semigroup associated to the absorbed process is exponentially ergodic with respect to a $\psi$ -distance.