The government made the announcement after the OAS voted to hold a meeting of foreign ministers to discuss the spiralling crisis in Venezuela.
Neighbours have expressed concern at mounting unrest in the country.
Violent protests against the government continued in the capital Caracas on Wednesday, with one protester killed.
He was hit by a tear gas canister during clashes with police.
Nearly 30 people have been killed since the wave of protests against President Nicolas Maduro began last month.
The Venezuelan government has accused the US of trying to undermine Mr Maduro's Socialist Party.
On Wednesday, Ms Rodriguez said the protests were part of an organised effort to defeat Venezuela's Bolivarian Revolution.
"Tomorrow [Thursday] we will present a letter of complaint to the OAS and we will begin a process that will take 24 months," she announced in a televised statement.
BBC Latin America correspondent Will Grant says the move comes as little surprise.
Tensions in the organisation - and among Venezuela's neighbours - have grown over what is seen by several member states as the government's disregard for democracy amid mounting unrest.
Venezuela OAS exit stirs regional concern, by BBC Monitoring
Venezuelan President Nicolas Maduro and allies hailed his 26 April decision to withdraw his country from the OAS as a "break with imperialism", but other OAS members worried the move would leave Venezuela isolated.
Uruguayan president Tabare Vasquez strove to find middle ground, saying "we do not think Venezuela should be isolated."
"It needs to be offered a hand," President Vasquez said.
Argentina's foreign minister, Susana Malcorra, tweeted that mediation was needed in Venezuela.
State media in Cuba, which was expelled from the OAS in 1962, highlighted President Maduro's denunciation of "interventionist abuses" by the organisation.
Ms Rodriguez accused the OAS of having double standards by concentrating on what was happening in her country while ignoring alleged democracy violations in Brazil.
President Maduro has often strongly denounced the grouping.
Venezuela, an oil-rich nation, is going through a serious economic crisis.
Inflation is expected to reach 700% this year, according to the International Monetary Fund, and there is shortage of many basic goods, including medicines.
The opposition blames the socialist policies of Mr Maduro and his predecessor, Hugo Chavez, for the economic meltdown.
But the government says the country is suffering from the effects of economic sabotage carried out by the business elite.
The latest series of protests began after the Supreme Court took over powers from the opposition-controlled National Assembly on 29 March.
It reversed its decision three days later, but opposition protesters were already on the streets in large numbers, seizing the opportunity to strike against Mr Maduro's government.
The opposition wants early elections and the release of politicians arrested since the president took office in 2013.
Thousands of his supporters held a counter-rally in Caracas on Wednesday.
|Anti-government protesters in Caracas on Wednesday were met with tear gas and rubber bullets|
Venezuela to withdraw from OAS, denounces campaign by Washington
Venezuela said on Wednesday it was withdrawing from the Organization of American States, deepening the diplomatic isolation of the socialist-run nation that is already out of step with Latin America's steady shift to the right.
Critics of President Nicolas Maduro have said Venezuela could be expelled from the group, accusing his government of eroding the country's democracy by delaying elections and refusing to respect the opposition-led Congress.
Venezuela said the move was a response to a Washington-backed campaign against the ruling Socialist Party that is meant to trample on the sovereignty of Venezuela, the United States' principal ideological adversary in the region.
"Tomorrow, as ordered by President Nicolas Maduro, we will present a letter of resignation from the Organization of American States, and we will begin a procedure that will take 24 months," Foreign Minister Delcy Rodriguez said in a televised statement.
The announcement came after the OAS agreed on Wednesday to hold a meeting of foreign ministers to discuss the situation in Venezuela. Maduro had warned on Tuesday that Venezuela would quit the group if the meeting were called.
The decision extends Venezuela's drift toward the fringes of international diplomacy. But the limited influence of the OAS means its exit will have few economic implications for the OPEC nation that is already struggling under triple-digit inflation, chronic product shortages and a crippling recession.
More than 15 years of diplomatic tensions between Caracas and Washington have done little to disrupt the flow of oil and fuel toward U.S. shores.
The OAS, once dominated by influential leftist governments from countries such as Argentina and Brazil, has clashed for months with Venezuela. Recent changes in governments in both countries brought in leaders openly hostile toward Maduro.
OAS chief Luis Almagro has said Venezuela should be suspended if it does not hold general elections "as quickly as possible."
Maduro's government calls the OAS a pawn of U.S. policy and dismisses Almagro, a former Uruguayan foreign minister once friendly with Venezuela's socialists, as a turncoat working for Washington.
Maduro's adversaries accuse him of delaying elections to avoid suffering ballot-box defeats, disregarding the country's opposition-led Congress and overseeing an economic crisis that has left the many in the country unable to eat properly.