The Doctor's TARDIS had a sickbay. (TV: The Invasion of Time, Cold Blood, AUDIO: The Blood Furnace) It may have been as big as an entire hospital ward. (PROSE: Sanctuary)
The Seventh Doctor treated Melanie Bush in the sickbay after she was injured by an explosion in the console room. (AUDIO: The Blood Furnace) In the Eleventh Doctor's TARDIS, this was up the stairs, to the left, then left again. It apparently had medical supplies to heal Mo from live vivisection. (TV: Cold Blood)