The Dor Alon fuel company, in coordination with the IDF, has stopped supplying fuel to gas stations in Gaza following Hamas's recent military takeover of the Strip.
Nevertheless, the company was still providing fuel to Gaza power stations.
Residents said the move would halt all traffic in the coastal strip, whose 1.3 million residents already face shortages of food and other essential supplies. Shipments into the territory dried up with the outbreak last week of fighting between Hamas and Fatah, which ended in Hamas's takeover of Gaza.
Asef Hamdi, a worker at a Gaza gas station, worried that what the end of the fuel shipments will mean for the territory.
"The results will be Gaza in full darkness, with no cars," he said. "In simple words... welcome to the Taliban lifestyle".
A spokeswoman for Dor Alon, who said company rules forbade giving her name, said the halt in shipments to the gas stations would take effect immediately, but supplies to the power station would continue as usual because the European Union guarantees the payment for those supplies.
IDF spokesman Shlomo Dror said Israel played no part in Dor Alon's decision and had no objection to humanitarian supplies crossing into Gaza, but the problem was that with the breakdown of civil authority there, Israel had no recognized party with whom to work.
"Hamas is running things, it's Hamas's responsibility," he said. "We are not interfering."
Meanwhile, some 300 Palestinians gathered at Erez Crossing on Sunday in an attempt to cross into Israel to escape the Hamas-controlled Gaza Strip.
In a similar incident on Saturday, IDF soldiers shot into the air to try to prevent the approaching crowds from infiltrating through the security fence.
Israel said that only a small number of "humanitarian cases" were being allowed to pass.
One family was allowed to enter Israel Sunday morning.
In related news, Israel Radio reported that Egypt sent many Fatah and Palestinian security officials who sought refuge in El-Arish back to the Gaza Strip. Some 200 officials left the Strip in boats for Egypt following the Hamas takeover.