A planning committee called the Legislative Administrative Council voted 4-3 to put Glas on trial in the congress.
The case now goes to the Constitutional Court and if it agrees, another panel in the National Assembly must vote on whether to let the entire body vote on dismissing Glas. A two-thirds majority is required.
Glas was sentenced Wednesday to six years in prison for receiving illegal kickbacks from Brazilian construction giant Odebrecht.
Glas, 48, had been in preventive custody since October, after his immunity was lifted by Congress, although he was allowed to remain vice president.
Prosecutors said Glas received a total of $13.5 million in Odebrecht bribes, via an uncle who is also under arrest. He was also charged with criminal association.
He is the highest-ranking Latin American politician to be convicted in the sprawling case centered on Odebrecht, whose past practice of giving bribes to secure public works contracts has cast a cloud over officials and ex-officials in several countries of the region.
Under investigation by the US Justice Department, Odebrecht agreed in December to pay a record $3.5 billion fine after admitting to paying $788 million in bribes across 12 countries to secure contracts.
The scandal has ensnared politicians in several countries, including Mexico, Peru, Panama and Venezuela.
Ecuadoran prosecutors said Odebrecht spent $47.3 million in bribes in their country to get public contracts.