"The decision has dealt the final blow to democracy in the country," said the Organisation of American States.
The court ruled that the assembly was in contempt and said it would exercise congressional functions.
The charge stems from alleged electoral irregularities by three opposition lawmakers in elections in 2015.
The head of the OAS Luis Almagro accused President Nicolas Maduro's government of carrying out what he described as a coup against itself.
Brazil's foreign ministry said the court's decision violated the country's separation of powers.
Several other Latin American countries expressed concern too.
Peru recalled its ambassador to Caracas, saying there had been a rupture of democracy.
The United States also condemned Venezuela's government.
"This rupture of democratic and constitutional norms greatly damages Venezuela's democratic institutions," said a State Department spokesman, Mark Toner.
Venezuela's opposition had earlier said President Maduro was becoming a dictator.
Venezuela's foreign ministry accused critics of the government of forming a right-wing regional pact against President Maduro.
He says the OAS is a pawn of US "imperialism".
There has been growing criticism of Venezuela's government after the Supreme Court took over legislative powers from the National Assembly.