"He [Aissami] is wanted for international narcotics trafficking", ICE said via Twitter.
ICE said El Aissami has facilitated shipments of narcotics from Venezuela with final destination in the United States and Mexico.
"In his previous positions, he oversaw or partially owned narcotics shipments of more than 1,000 kilograms from Venezuela on multiple occasions, including those with the final destinations of Mexico and the United States", ICE said on its website.
Each of the five counts with which El Aissami has been charged carries a maximum penalty of 30 years in prison.
In March, a US federal court indicted El Aissami for allegedly trafficking drugs and violating sanctions imposed on Venezuela.
El Aissami currently serves as Minister of Industry and National Production in Venezuela.
Venezuela has been suffering a humanitarian and political crisis that intensified in January when US-backed opposition leader Juan Guaido illegally declared himself the country’s interim president after disputing Nicolas Maduro's re-election.
The United States and some other countries have recognized Guaido. However, Russia, China, Cuba, Bolivia, Turkey and a number of other countries have said they recognize constitutionally-elected Maduro as the only legitimate president of Venezuela.