One source, quoted by the energy reporting service Platts, said on Monday that a vessel seeking an 800 metric tonne (mt) bunker stem had been unable to find a supplier.
Reports say there are still four large bunker barges and three marine gas oil (MGO) barges operating in the port.
Novorossiysk is a major oil export port and a regional bunker hub. Around one million metric tonnes (mt) of marine fuel are sold each year.
Bunker deliveries are made by barge and from ex-pipe facilities at the Sheskharis Oil Terminal.