Carvaja was expected to make a court appearance on Friday. U.S. officials have 60 days in which to request his extradition.
The U.S. Treasury Department has accused Carvajal of "materially assisting the narcotics trafficking activities of the Revolutionary Armed Forces of Colombia (FARC)."
Venezuela's foreign ministry has denounced the former military intelligence chief's arrest.
"The Venezuelan government strenuously rejects the illegal detention of its diplomatic official, carried out by Dutch officials in Aruba in violation of international laws."
Caravajal was nominated to serve as consul general in Aruba. Because his appointment had not yet been confirmed by Venezuelan President Nicolas Maduro, Aruba's prosecutor general's office maintains diplomatic immunity does not apply in this case.