The fuel crisis has already led to frequent power cuts in Tehran in recent weeks and nationwide closures of schools and businesses.
The Tehran Chamber of Trade Unions and Guilds has decided that malls and shopping centres would close at 8:00 pm (1630 GMT), instead of their usual time of 10:00 pm, according to a statement carried by news agency ISNA.
State TV quoted the head of the organisation, Hamidreza Rastegar, as saying that "if malls fail to abide by the new decision, their gas and electricity supply will be cut and they will be shuttered."
It was unclear how long the measure would remain in effect.
Energy giant Iran has one of the world's largest reserves of natural gas, but it has been forced to ration electricity in recent weeks due to a lack of gas and fuel to feed its power plants.
The energy crisis comes as sub-zero temperatures have been recorded across Iran in recent days.
Schools and public offices were closed down on Tuesday in more than half of Iran's 31 provinces, for the third consecutive day, "due to the cold weather and in order to manage fuel consumption", official news agency IRNA said.
On Monday, President Masoud Pezeshkian lamented the "very high" energy consumption in Iran.
"We consume more than two to three times the electricity and gas compared to European countries," he said, according to state media.
Pezeshkian encouraged Iranians to reduce their reliance on home heaters and suggested wearing warm clothes as an alternative.
