The move is the latest escalation in the Trump administration's campaign against The Hague-based court, which was established in 2002 by the international community to prosecute war crimes, genocide and crimes against humanity.
The US is not a member of the court.
Rubio said in a statement he was imposing sanctions on Tomoko Akane, a Japanese judge who is president of the ICC, and Abdoulaye Seye, a senior trial lawyer and a Senegalese national, under a Trump executive order last year authorising sanctions against the court.
"These individuals have directly engaged in efforts by the ICC to investigate, arrest, detain, or prosecute officials whose government has not consented to ICC jurisdiction," Rubio said.
The ICC condemned the move, saying in a statement the measures undermine the rule of law.
"When judicial actors are threatened for applying the law, it is the international legal order itself that is placed at risk," the ICC said.
Seye is a senior trial lawyer on the prosecution team that sought an arrest warrant for Israeli Prime Minister Benjamin Netanyahu, and has been nominated for election as an ICC judge.
The US effort has put it at odds with allies in Europe. Dutch Foreign Minister Tom Berendsen said on X the Netherlands, which hosts the court, disapproved of the latest US sanctions and he had invited Akane to "discuss our continued support."
"International courts and tribunals must be able to freely carry out their mandates," Berendsen wrote.
Top ICC judge Akane warned in December that the US sanctions would "rapidly undermine the court's operations in all situations and cases, and jeopardise its very existence".
The US imposed targeted sanctions last year on several ICC officials, including prosecutors and judges, citing the ICC's arrest warrants for Netanyahu and former Israeli Defense Minister Yoav Gallant, as well as a past probe into US troops in Afghanistan.
The sanctions freeze any US assets the individuals may have and essentially cut them off from the US financial system, with which almost all internationally operating banks have close ties.
The US Treasury Department also issued a general licence on Tuesday authorising the wind-down of transactions involving Akane and Seye through September 17.
Three ICC judges sued Trump and his administration in June over the sanctions, arguing the measures were unlawful.
Advocacy groups, in two separate lawsuits, have said the US campaign infringes on the constitutional rights of organisations working with the court to seek justice for atrocities around the world.
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