In a televised address, Mr Maduro said the man was seized with weapons and large sums of money near the Amuay and Cardon refineries on Thursday.
He said the man was “serving as a navy on CIA bases in Iraq.” He gave no further details.
The United States has so far made no public comment on the matter.
Meanwhile, Maduro said Venezuelan authorities recently foiled a plot to cause an explosion at the El Palito refinery in northern Carabobo state. He didn’t elaborate.
Last month, a Venezuelan court sentenced two former US soldiers to 20 years in prison for trying to overthrow Mr. Maduro.
Luke Denman and Airan Berry were convicted of conspiracy, arms trafficking and terrorism.
The couple were among 13 people arrested in May as they tried to enter Venezuela by sea from Colombia.
US President Donald Trump, a longtime opponent of Socialist President Maduro, has denied Venezuela’s accusations that he was behind the incident.
Washington supports opposition leader Juan Guaidó and recognizes him as the country’s legitimate leader.
Relations between the United States and Venezuela are strained. Mr. Maduro accused America of manipulating the political opposition to steal the country’s vast oil wealth.
America and Mr. Guaidó, meanwhile, blamed the president for Venezuela’s economic collapse.