The agency says test results will not be known for 24 hours and health officials are trying to identify potential exposure sites.
The individual under investigation is in self-isolation at home. It is not known if this person is a child or an adult.
According to the Centers for Disease Control and Prevention, this would be the first reported case of the measles in Virginia in 2015. There were only two reported case in Virginia in 2014.
Dating back to Dec. 28, 114 people from seven states were reported to have the measles. The CDC says that many of the cases are linked to a mid-December outbreak at Disneyland in Anaheim, Calif.
The United States experienced a record number of measles cases during 2014, with 644 cases from 27 states. According to the CDC, this is the greatest number of reported cases since measles elimination in 2000. From 2001 to 2011, the average number of reported cases per year was around 60.
The CDC reports that since Jan. 1., there have been 121 reported cases.
Health officials reminded the public that people who have received at least one dose of measles, mumps and rubella (MMR) vaccine in the past are at very low risk of being infected with measles. And, the best protection against future measles cases is the on-time vaccination of all susceptible people.
Measles is a highly contagious illness that is spread through coughing, sneezing and contact with secretions from the nose, mouth and throat of an infected individual.
Symptoms usually appear in two stages. In the first stage, most people have a fever of greater than 101 degrees, runny nose, watery red eyes and a cough. The second stage begins around the third to seventh day when a rash begins to appear on the face and spreads over the entire body.
If the case in question is positive, a news conference will be held on Wednesday.
For those whose children are not vaccinated, health officials are urging parents to avoid attending "measles parties" for kids, where an unvaccinated child is exposed to at least one infected person. Parents attend the parties, rather than vaccinating their children or leaving things up to chance.