Maduro, 56, was sworn in for a second term on Thursday, having won a highly controversial election in May that was boycotted by the opposition and branded a fraud by the United States, European Union and Organization of American States.
The National Assembly's president Juan Guiado said the constitution gives parliament the right to assume transitional power after declaring Maduro a "usurper," but said it would need military backing and for people to take to the streets to demand change.
"Is it enough to lean on the constitution in a dictatorship? No. It needs to be the people, the military and the international community that lead us to take over," said Guiado, speaking to around a thousand opposition supporters in Caracas.
Parliament pointedly announced the significant date of January 23 for its mass protest as this was the day in 1958 in which the military dictatorship of Marcos Perez Jimenez fell.
The National Assembly, like many foreign countries, has dismissed Maduro's election as illegitimate but parliament has been sidelined by the president's power grab.
Having lost control of parliament in 2016, Maduro last year created a rival Constituent Assembly filled with loyalists while his allies at the Supreme Court stripped parliament of its powers.
Maduro's swearing in ceremony was even held at the Supreme Court rather than parliament.
The hand-picked successor to late strongman Hugo Chaves also has the backing of the military high command, which reiterated its "loyalty" to the president on both Wednesday and Thursday.