The country's highest court ordered the preventive detention along with a freeze of Glas' assets and bank accounts on Monday.
Under investigation by the US Justice Department, Odebrecht agreed in December to pay a record USD 3.5 billion fine after admitting to paying USD 788 million in bribes across 12 countries to secure juicy tenders.
Glas is just the latest political figure in Latin America to be identified as a suspected recipient of bribes from the Brazilian group.
Ecuadoran lawmakers in August unanimously voted to allow the corruption probe against Glas to go ahead. He was barred from leaving the country.
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Glas, who was minister of strategic sectors before becoming vice president in 2013, has denied any link to the Odebrecht scandal, though his uncle, Ricardo Rivera, has been arrested for his alleged participation in the affair.
"I acknowledge UNDER PROTEST this detestable outrage against me, though I am confident justice will prevail and that I will prove my innocence," Glas tweeted after the court order.
Eighteen Ecuadorans including Glas and Rivera face court over the Odebrecht matter. So far, there have been no convictions.
Prosecutors are to formally present their charges against Glas in coming days.
Their case relies at least in part on information given by a former Odebrecht employee, Jose Concericao Santos Filho, who said Glas received USD 16 million in bribes via Rivera.
Ecuador's president, Lenin Moreno, stripped Glas of many of his powers as the two men engaged in a bitter dispute.
Moreno can designate a temporary vice president from among his ministers.
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