The sailor is one of only a handful of women living in the barracks.
Cause of death is still under investigation, but a senior defense official said there was "definitely foul play" involved, NBC News reported. The official confirmed that the young sailor worked at the Pentagon.
Fort Myer is the military base next to Arlington National Cemetery.
The Fort Myer Military Community released the following statement:
"An investigation is under way after a servicemember was found deceased in a barracks room this morning at Joint Base Myer-Henderson Hall. The individual was discovered this morning after not reporting to work last night as expected. As this investigation is beginning and details are just emerging, it would be inappropriate to offer additional comments at this time."