WASHINGTON—Thousands of U.S. troops are likely suffering traumatic brain injury not just from battlefield explosions but from repeated exposure to trauma while training on their own weapons, according to a new study.

Service members, even those who may not have seen combat but specialize in using high explosives or weapons such as rocket launchers, could have lasting brain damage from the pounding on their necks and heads, researchers at the Center for a New American Security said in a report released Monday. The defense think...