"We exhort the United States to return to the realm of international law, end its politics of blackmail and stop provoking tensions in Venezuela from abroad," the foreign ministry said in a statement.
"Washington has repeatedly displayed a categoric refusal to adopt the method of negotiation to resolve the situation," it said.
The ministry termed the latest sanctions "a brutal attempt to pressure the government of this country and the Venezuelan people."
US targets Cuba's oil supply from Venezuela in new sanctions
The US earlier said any American assets of Arreaza would be blocked.
The sanctions are the latest slapped by Washington against senior figures in Venezuela as it seeks to install in power Juan Guaido, the opposition leader.
But while most previous sanction announcements alleged corruption or rights violations by the officials, the Treasury Department did not cite any specific violations by Arreaza, instead saying he was targeted for his role as foreign minister.
Arreaza, a former journalist who studied at Cambridge, has travelled several times to New York to represent Venezuela at the United Nations since the United States and most Latin American countries in January declared Maduro to be illegitimate.
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