U.S. President Donald Trump's administration has threatened Maduro's government with a harsh response should it ever detain Guaido.
The opposition said Mr Maduro had stacked the court with his own supporters. About 50 countries, including the United States and much of Latin America, have recognised Guaido as the country's legitimate leader.
Edgar Zambrano, the deputy speaker of the opposition-majority National Assembly, was jailed for "the flagrant commission of the crimes of treason, conspiracy and civil rebellion", the court said.
This brings to 10 the number of opposition lawmakers indicted for supporting Guaido, following a court announcement on Tuesday that seven others will be prosecuted.
"I thank Italy for the welcome", De Grazia wrote on Twitter, though he did not say he had taken refuge in the embassy, Reuters report says.
Venezuelan intelligence agents on Wednesday detained a senior leader of the opposition-controlled Venezuelan National Assembly, the first arrest of a lawmaker since a failed uprising against Venezuelan President Nicolas Maduro last week. He tweeted that he was being taken to the SEBIN headquarters in Caracas.
Soley Zambrano, his daughter, said she last heard from her father around 6:30 p.m. on Wednesday.
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.
"We warn the people of Venezuela and the worldwide community: the regime has kidnapped the first vice president" of the assembly, said Guaido, who has been in a power struggle with Maduro since declaring himself the nation's acting president in January.
The decision to strip legislators of their immunity and to arrest Zambrano was condemned as "unconstitutional" in a statement on Thursday by the regional Lima Group bloc.
Last week, Leopoldo Lopez - Guaido's political mentor - moved into Spain's diplomatic residence after escaping house arrest to appear alongside Guaido during his call for the military to rise up.
But Maduro retains control of the military and state functions.