During a televised address, Justice said the patient is in the Eastern Panhandle, which is close to Washington, D.C., but he did not specify which county.
"We have a real plan, we developed a plan of preparedness. And from that, a plan of action," he said.
Justice ordered all state restaurants, bars and casinos to close, but said carryout food services will remain available.
The West Virginia Republican also called for calm in the face of the outbreak and said citizens should continue to live their lives, but with a sense of vigilance and caution.
"We've prepared for this and we shouldn't panic. We should be cautious, we should be concerned, but we should not panic," he explained.
"We should go ahead and try to live our lives as best we can, but again, we should not panic. We should not be fearful, we should not be afraid. We should be smart at this time. We should absolutely not be weak."
While addressing the recent economic instability, Justice called President Trump a "real friend" who's invested in protecting the economic prosperity of the state and the country and said state and federal officials will work to make people financially whole.
"We're all in this boat together," he added. "We're going to win. We're going to beat this bad, bad disease. Thank you in every way. God bless you."