Maduro identified the American as the Air Force attache and said he had been spying on the military.
He said the official has 24 hours to leave the country.
Embassy spokesman Greg Adams identified the attache as David Delmonaco.
Adams had no immediate comment.
"I'm sure we will be formulating some sort of response from Washington," he said.
He said he did not immediately know Delmonaco's rank.
Maduro spoke hours after the government said Chavez was in "very delicate" health after undergoing cancer surgery in December.