Medical leave, or medical rest leave, was a term in Starfleet which described shore leave at medical order. According to Starfleet regulations, an officer taking medical leave could select their rehabilitation facility.
In 2254, Doctor Phil Boyce advised Captain Christopher Pike to take his rest leave but Pike considered leaving the ship instead. (TOS: "The Cage") Sometime prior to 2257, Pike took medical leave, a fact which was listed, along with the afflictions he experienced during his lifetime, in the medical history section of his personnel file. (DIS: "Brother")
In 2375, Ensign Nog was ordered to take medical leave by Starfleet Command after he lost a leg in the battle of AR-558. Upon his return to Deep Space 9 Captain Benjamin Sisko read the orders from a PADD and told Nog that his medical leave was granted with the exception of his participation in his welcome home party in the wardroom. (DS9: "It's Only a Paper Moon")