Denmark's Maersk Line will stop shipping, or accepting payment for, cargo linked to Russians on the US' specially designated nationals (SDN) list.
It said in a customer note that the decision followed the tightening of sanctions against Russian individuals and companies.
Cargo linked to the SDN list is prohibited on US vessels or at US ports.
The new measures target Russian oligarchs including Oleg Deripaska, owner of industrial groups Basic Element, and Viktor Vekselberg, owner of conglomerate Renova Group.