Shortly before his arrest, Zambrano said on Twitter that agents of the SEBIN intelligence agency had encircled his vehicle outside the headquarters of the Democratic Action party.
Venezuela's Supreme Court had authorized legal actions against the seven who have been charged with conspiracy, rebellion, and treason, among others.
Zambrano, opposition leader and self-declared President Juan Guaido's deputy as National Assembly speaker, was detained by agents in Caracas for backing the failed April 30 military uprising against President Nicolas Maduro, which was orchestrated by Guaido. The United States, which has imposed sanctions in Venezuela's oil industry, has warned of severe repercussions if Maduro moves against the man he has described as a collaborator in a USA -engineered coup plot.
"As we refused to get out of our vehicle, they used a tow truck to forcibly take us directly to El Helicoide", he said, referring to a notorious political prison and the headquarters of the secret service.
He was transferred to the Caracas headquarters of the military police, Fort Tiuna, the court said.
About 50 countries, including the United States and much of Latin America, have recognized Guaido as the country's legitimate leader.
The Venezuelan regime has begun a purge of suspected defectors and opposition politicians after last week's failed uprising against President Maduro.
Three others - Richard Blanco, Mariela Magallanes and Americo De Grazia - have sought refuge in the Argentine and Italian embassies in Caracas. Maduro, who was re-elected a year ago in a disputed vote, has presided over an economic collapse and humanitarian crisis in Venezuela.
The decision to strip legislators of their immunity and to arrest Zambrano was condemned as "unconstitutional" in a statement on Thursday by the Lima Group, a regional bloc comprising Argentina, Brazil, Chile, Peru, Colombia and Canada.
The judicial measure against Zambrano was dictated after he was apprehended once his parliamentary immunity had been raided by the National Constituent Assembly, and by virtue of the provisions of the Constitution of the Republic, for being implicated in the attempted coup d'état.
Secretary of State Mike Pompeo announced that the USA has a "full-scale set of options" to resolve the Venezuelan crisis, claiming that any actions that the U.S. takes in the country would be "lawful".
Pence said the United States was lifting economic sanctions on a former Venezuelan general who turned against Maduro in order to encourage other Maduro allies to follow suit.
"The European Union calls for Edgar Zambrano's immediate release and holds the relevant authorities responsible for his safety and integrity".