This paper presents a statistical approach to adapt out-of-domain machine translation systems to the medical domain through an unsupervised post-editing step. A statistical post-editing model is built on statistical machine translation (SMT) outputs aligned with their translation references. Evaluations carried out to translate medical texts from French to English show that an out-of-domain machine translation system can be adapted a posteri-ori to a specific domain. Two SMT systems are studied: a state-of-the-art phrase-based implementation and an online publicly available system. Our experiments also indicate that selecting sentences for post-editing leads to significant improvements of translation quality and that more gains are still possible with respect to an oracle measure.