Mr Guaidó then raised his right hand and said: "I swear to formally assume the national executive powers as acting president," vowing to lead a transitional government and hold free elections.
He called on the armed forces - who have so far backed Mr Maduro - to disobey the government.
Venezuelan NGOs said that 14 people were shot dead during protests on Tuesday and Wednesday.
How did the US respond?
President Donald Trump recognised Mr Guaidó as interim president in an apparently co-ordinated move minutes after the 35-year-old declared himself acting leader.
In a statement, he described Mr Maduro's leadership as "illegitimate", adding: "The people of Venezuela have courageously spoken out against Maduro and his regime and demanded freedom and the rule of law."
It warned Mr Maduro not to threaten the safety of the Venezuelan people and said tougher sanctions could be imposed.
Mr Trump told journalists he was not considering military action but added that "all options are on the table".
He called on other nations to follow suit in supporting Mr Guaidó.