The body was found in a wooded area on the Camp Lejeune base. Officials are not allowing access to the general crime scene.
"The victim did not die from a gunshot wound," US Marine Corp Capt. Timothy Patrick said. "But other than that, we don't have any other information."
Military officials are releasing few details, but the Marines say the 21-year-old suspect also tried to hurt himself.
Officials are not ready to call it a murder, suicide attempt and no charges have yet been filed. Law is not in jail, but is hospitalized.
"He was being treated for what is apparently self-inflicted wounds," Patrick said. "The nature of those wounds I don't have."
Officials say Law was a supply administration clerk assigned to 2nd Supply Battalion, 2nd Marine Logistics Group, II Marine Expeditionary Force. He was deployed to Iraq from August 2007 to March 2008.
A spokesperson says the incident is under investigation and did not have more information about what happened. They did say their investigation will also ask if it may be related to any sort of combat stress.