Fuel shortages since the superstorm hit have led to hours-long waiting times at pumps, and traffic chaos for commuters struggling to get to work.
Similar measures were introduced in New Jersey on Saturday and will also be enforced in New York’s Long Island.
Only 25% of New York’s petrol stations are operating, Michael Bloomberg said.
Under the rationing system, cars with licence plates ending in odd numbers will be allowed to buy fuel only on odd-numbered days of the month; cars with even numbers at the end of their licence plates will be allowed to buy petrol on even-numbered days.
“We have to do something, and this is something that is practical and enforceable and understandable, and doing something is a lot better than doing nothing,” Michael Bloomberg said.
But the owner of one petrol station was more cautious.
“It’s more pressure on us,” Ash Gaied said.
“They yell. They curse. You wouldn’t believe it.”
The rule will come into effect at 06:00 EDT on Friday, the mayor announced.
New York City’s yellow taxis and emergency vehicles are exempt from the rationing rules.
Sandy – which started as a hurricane but was dubbed “Superstorm Sandy” as it moved inland – struck the US East Coast on Monday last week.
It devastated parts of New Jersey and New York, causing record flooding and widespread power cuts.
More than 100 people were killed as the storm barreled inland across Pennsylvania, and estimates suggest Sandy may have caused between $30 billion and $50 billion in property damage and lost business.
A unseasonably early snowstorm that hit New York on Wednesday has compounded the misery for some residents in the area, who have yet to regain electricity since being were cut off last week.
Parts of neighboring Connecticut saw more than 1ft (30cm) of snow on Wednesday, and wind speeds of as much as 50 mph (80 km/h) – and resulted in power cuts for about 300,000 customers.
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