Longman Dictionary of Contemporary English
Wiktionary
n. An injury which pierces the skin and causes bleeding, but which does not injure any bones or vital organs, and does not carry a serious threat of death.
WordNet
n. a wound that does not damage important internal organs or shatter any bones
Usage examples of "flesh wound".
Here he was acting like a big baby over a sore arm and a flesh wound, while the knight had probably been given enough poison to kill a brothelful of whores.
A fine slick of blood was running down her flank from the flesh wound his ball had inflicted.
DeWayne Buchanan had suffered a slight flesh wound in the upper arm when Ronnie Campbell neglected to raise hispistol high enough while carousing on the riverbank, but was in good spirits after having the wound cleaned and dressed.
I could have killed him without any trouble at all but thought that a painful flesh wound would suffice.
I cut him on the left breast, leaving his jacket tattered and blood weeping from a flesh wound.