The Venezuelan regime has begun a purge of suspected defectors and opposition politicians after last week's failed uprising against President Maduro.
The US, Canada, some Latin American and European nations were quick to recognize Guaido as the new legitimate leader of Venezuela and have supported him in his attempts to oust Maduro from power.
On Wednesday, Edgar Zambrano, the opposition-run National Assembly's vice president, said he had been arrested by intelligence agents.
"We warn the people of Venezuela and the global community: the regime has kidnapped the first vice-president" of the National Assembly, said Guaido, who heads the body and has been in a power struggle with Maduro since declaring himself acting president in January. If he is not immediately freed, there will be consequences, ' the embassy said on Twitter.
Zambrano was transferred to the headquarters of the military police in Caracas's largest military complex, Fort Tiuna, the court said.
Tensions escalated when Guaido, who heads Venezuela's National Assembly, declared himself acting president on January 23, a move which was supported by the US and many European and Latin American countries. "He was one of the main [leaders] of the coup", Maduro's second-in-command, Diosdado Cabello, said on television, according to the Guardian.
Guaido called for a national demonstration on Saturday to reject measures taken by the Supreme Court against opposition lawmakers.
US President Donald Trump - whose government was among the first to back Juan Guaido - said he was "discussing the awful abuses by Maduro". The auto was towed, with him inside, to Caracas' notorious El Helicoide prison, the Guardian reports.
National Assembly Vice President Edgar Zambrano was leaving his Democratic Action party's headquarters when he was surprised by a commando unit from the feared SEBIN intelligence agency who surrounded his auto.
"All united to vote and win", in Caracas, Venezuela, Wednesday, May 8, 2019, after National Assembly Vice President Edgar Zambrano was arrested when leaving the headquarters.
"This assault on the National Assembly should serve as a clarion call to the region and the world that the dictatorship is not interested in constitutional solutions to the Venezuelan people's problems".
The Constituent Assembly had already lifted Guaido's immunity in April, accusing him of trying to "usurp" the presidency.
U.S. Vice President Mike Pence said on Tuesday the Trump administration would soon sanction the 25 remaining members of the court.
The Constituent Assembly, a body set up by Maduro to outflank the opposition-led National Assembly, followed up by stripping seven of the deputies of their parliamentary immunity.