The company that ships Yukos's oil by river is refusing to ship crude on credit although transport fees have been paid until the end of August.
"We are not ready to transport Yukos oil on credit because it is unclear who will then be paying for our services," Mr Alexander Alexandrovich, chairman of Volgotanker, said.
He added the port of Kavkaz on the Black Sea, to which Yukos usually supplies up to 100,000 barrels per day of crude by Volgotanker, would be most affected.
Yukos owned Volgotanker, Europe's largest crude oil and refined products river carrier, until 2000 but later sold it in a management buyout.
Volgotanker ships around 200,000 barrels per day of oil and products from refineries in central Russia to major ports on the Black and Baltic Seas in small tankers by river for re-export in larger cargoes.
Yukos accounts for more than 50 per cent of Volgotanker's volumes.
Yukos must pay $3.4 billion in back taxes by the end of August - something the firm says it cannot do because it lacks spare cash and is forbidden from selling any of its assets to raise more money.
The company's bank accounts are also frozen, and Yukos says it may be forced to cut production and exports as it lacks necessary funds to pay for basic operational needs, such as oil transportation fees.