The country's constitution bars Germany from extraditing its citizens.
The company itself has now pleaded guilty to a similar array of criminal charges, in a $4.3 billion deal it signed with numerous regulatory agencies this week in the waning days of the current presidential administration.
In 2015, federal officials revealed that Volkswagen was deliberately skirting emissions testing for some of its diesel vehicles.
Schmidt is the first high-profile Volkswagen executive to have been arrested since news of the scandal broke. They returned to Miami and spent theholidays with friends.
Schmidt, who is caught up in the "Dieselgate" investigation by the U.S. Department of Justice (DoJ), was ordered to be charged and held without bail on Thursday pending trial.
U.S. Magistrate Judge William Turnoff of the U.S. District Court for the Southern District of Florida found that Mr. Schmidt, 48 years old, posed a flight risk given the seriousness of the charges against him and the fact that he was born and lives in Germany.More news: JPMorgan's Dimon Sees Economic 'Momentum' Building as Trading Surges
Oliver Schmidt headed Volkswagen's regulatory compliance office in the United States from 2014 to March 2015. The scheme involved software that produced acceptable emission levels in US environmental tests but much higher amounts when the vehicles were driven on the roads.
Justice Department trial attorney Ben Singer also said Schmidt also was deceptive when he voluntarily met with Federal Bureau of Investigation agents in London, England, in November 2016. Prosecutors are concerned because if Schmidt were to return to Germany, there would be no way for the U.S.
Among green technologies, Moonraker-and Schmidt-concluded that Volkswagen should emphasize plug-in hybrids.
Schmidt and five other Volkswagen executives were charged Wednesday in an indictment released in Detroit with playing key roles in VW's scheme to knowingly sell almost 600,000 diesel vehicles that did not meet US pollution emissions standards.
They are charged with alleged violations of the country's Clean Air Conservation Act, related to emissions cheating with the "defeat device" software.