Heredia blamed her manager at the time for not scheduling concerts or public appearances.
Duran said police are interrogating Heredia to determine whether she was working as a mule for a drug-trafficking organization.
General Prosecutor Francisco Dominguez issued a statement saying Heredia's situation was unfortunate.
In December 2010, Heredia hit and killed a teenage Haitian boy with her car as he tried to cross a highway by foot.
Dozens of fans greeted Heredia when she returned to the Dominican Republic after her win, and Fernandez invited her to the National Palace.
Police also ordered Heredia to undergo X-ray tests to determine whether she had any drugs hidden inside her body, but none were found.
Prosecutor Luisa Liranzo said Heredia does not yet have an attorney.
Jorge Heredia, who has been in San Quentin 15 years and is serving 13 year to life for attempted murder, previously sold produce before going prison.
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But Heredia, nicknamed "La Baby" because of her penchant for calling people "baby", disappeared shortly after all the fanfare, drawing speculations including that she was pregnant.
Heredia did something similar on his own prior to going to prison but says after the Last Mile program he is better prepared to run the business.
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Heredia's name disappeared once again and resurfaced last month when she filed a domestic violence complaint against her husband, Manuel Varet Marte, a hip-hop singer known as Vakero.
Martha Heredia was arrested late Wednesday as she was about to board a plane to New York, said Frank Duran, the National Drug Control Agency's director for the city of Santiago.
The TV station also featured an interview with Heredia, who said she granted the interview because she was tired of the rumors surrounding her disappearance from the local show business industry.
On the night Heredia vied for the title, thousands of Dominicans gathered in public plazas to watch her sing on huge TV screens, and then-President Leonel Fernandez urged Dominicans to vote for her.
However, many locals are convinced that Heredia is trying to hide the fact that her husband's party (PNP) would be receiving Chavista funds from Venezuela to finance his presidential campaign and aid the ALBA houses.
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