A rigid hull inflatable boat collided with the USNS Big Horn during the exercise, according to the Navy.
The Navy says the three civilians were instructors from the Center for Security Forces.
Six injured individuals were taken to Sentara Virginia Beach Hospital and one sailor was treated at Joint Expeditionary Base Little Creek, Va.
Two sailors have been released and another remains in the hospital for observation.
All injuries are considered non-life-threatening the Navy says.
There's been no word yet on the status of the three civilians and officials are now investigating this case.