A sprain was a term used to describe the tearing of one or more ligaments surrounding a joint.
In 2152, Dr. Phlox informed Captain Jonathan Archer that a few bruises and sprains were suffered when some of the Enterprise NX-01 crew lost consciousness as a result of unusual radiation from a trinary star system. (ENT: "Singularity")
In 2370, Major Kira Nerys failed to suffer so much as a sprain after a rash of minor accidents affected Deep Space 9; a number of other patients were not so fortunate. (DS9: "Rivals")
In 2371, Kathryn Janeway ordered Harry Kim to stand at ease before he sprained something, after the ensign stood too rigidly to attention upon meeting his captain for the first time. (VOY: "Caretaker")
In 2375, B'Elanna Torres likened feeling something by spraining her ankle to her efforts to experience feelings by running holodeck programs with the safety protocols off. (VOY: "Extreme Risk")
Later that year, the holographic character Vic Fontaine suffered three bruised ribs and a sprained left wrist after getting creamed by gangsters. (DS9: "Badda-Bing, Badda-Bang")