The last Civil War generals on either side to die of battle wounds, Federal Brevet Brigadier General Theodore Read and Confederate Brigadier General James Dearing received their fatal wounds during the Battle of High Bridge. Read died on the battlefield, Dearing died of his wounds a couple weeks later and a week after Confederate BG Robert C. Tyler was killed at the Battle of West Point (GA). Historians question whether Dearing's promotion to brigadier general had been confirmed by the Confederate Senate which makes the point debatable.
Civil War Union Brevet Brigadier General. An 1854 graduate of Indiana University, he practiced law prior to the outbreak of the Civil War. He entered the service as a private in the 12th Illinois Infantry but was soon commissioned and served in various staff positions finally becoming lieutenant...
Civil War Confederate Brigadier General. He was born in Campbell County, Virginia, and was a graduate of Hanover Academy. He entered West Point in 1858, however, he resigned from the Academy on April 22, 1861, after his native state seceded. Until the day he left the Academy, he was ranked first...
Answer: Union General Theodore Read was killed while mortally wounding CS General James Dearing in an exchange of pistol shots.
Source: The Civil War Book of Lists.
Edit - The question did not ask for the names of the two generals. So I'm going to be liberal in scoring this question and give credit to everyone who said that they engaged in a duel or shot each other or words to that effect, even if the answers don't include the generals' names.
The source that I used indicated that Read died on April 6 and Dearing died two weeks later. Several players provided sources in support of this. I was a little surprised that a number of players stated that the two generals both died on April 22. Nobody provided a source to support this contention, but nobody will lose credit, since the question didn't ask when the generals died.