Russia’s oil majors thought a new fuel-tax break this year would support the sector. Now, low demand for gasoline in Europe is turning what was expected to be a help into a multi-million-dollar hindrance.

“Russian oil companies have become hostages of external market conditions,” said Ivan Khomutov, chief executive officer of Moscow-based energy consultant Petromarket.

Weak gasoline prices in Europe have turned tax calculations upside down for Russian oil companies. Major producers may now have to pay as much as...