Ms Rodriguez accused Brazil of violating the rule of law and Canada of interfering in Venezuela's internal affairs.
Both countries have strongly criticised the move.
The decision to expel Ambassador Pereira may have been triggered by Brazil's recent complaint that President Nicolás Maduro was "constantly harassing the opposition".
Canada imposed sanctions on senior Venezuelan officials a few months ago.
'Rude and vulgar'
Venezuela's diplomatic relations with Brazil have deteriorated since Brazil's centre-right President, Michel Temer, replaced left-wing leader Dilma Rousseff.
Her impeachment was described by Mr Maduro as a "right-wing coup".
"Diplomatic relations with Brazil will not be restored until the government reinstates the constitutional order it has effectively broken," said Ms Rodriguez at a news conference on Saturday.
The Brazilian government said the move showed once again the authoritarian nature of President Maduro's administration.
Ms Rodriguez accused Mr Kowalik of "permanent and insistent, rude and vulgar interference in the internal affairs of Venezuela".
Relations with Canada have been difficult for months. Ottawa imposed sanctions on Venezuelan officials earlier this year for alleged human rights violations and corruption.
Foreign Minister Jorge Arreaza said in November that the sanctions were illegal and accused the Canadian government of "shameful and utter submission to Donald Trump's administration".
Canada responded to the expulsion of its charge d'affaires by saying it would not be cowed into easing pressure on the Maduro government.
Canada and Brazil were among many countries critical of Mr Maduro's decision to convene a Constituent Assembly, which effectively replaced the opposition-controlled National Assembly.
The announcement prompted mass street protests, which killed more than 120 people in four months.
The opposition boycotted the poll in July and also held an unofficial referendum in which they said more than seven million Venezuelans voted against the constituent assembly.
The European Union and major Latin American nations have said they will not recognise the new body.
The US imposed sanctions on Mr Maduro and the Trump administration labelled him a "dictator".
Mr Maduro's six-year term ends in 2019. He is due to run for re-election next year.
The opposition has accused Mr Maduro and his predecessor, the late Hugo Chavez, of destroying the country's economy with their socialist policies.
Venezuela has one of the world's highest inflation rates and for years has suffered from a shortage of basic goods, including medicines.
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