What is the name of an entity - a room or a couple rooms, or a small detached building serving the role of a tiny hospital within a larger entity (military base, prison, or even a ship.) Essentially, a place where the sick of the enclosed entity are treated, either for milder cases where actual hospital is not necessary, or when access to a real hospital is unavailable.
Aboard a ship, it is called a sickbay. Considering the definitions of it here http://dictionary.cambridge.org/dictionary/british/sickbay?q=sickbay and here http://www.ldoceonline.com/dictionary/sickbay, this might also be suitable to use when talking about such a room in general, even when it is on land.
According to this link http://www.ldoceonline.com/dictionary/infirmary, the word infirmary can used be used in general but, it does not include ships.