A few others are on the bed of the stream, The Washington Post reported. The Post said it alerted management at the cemetery to the headstones.
Arlington, the nation's leading military cemetery, has been hit by a recent scandal with allegations 200 people were buried in unmarked or incorrectly marked graves.
The Post said the new find is something of a mystery. The newspaper suggested they might have been replaced because they had become too weathered to read or have had spelling or other mistakes.
"They appear to be decades old," cemetery spokeswoman Kaitlin Horst said.