City hall said in a statement that the overall space taken up by cars had diminished thanks to its "determined action" but that the average size and weight of cars had gone up.
The vote, to be held in February, will be the second city-wide referendum on urban matters, after residents in April voted to ban rental e-scooters from the capital.
Sport Utility Vehicles (SUVs) can weigh 2,700 kilos or more, around a third more than regular automobiles.
"They're accident-prone, heavy, bulky and polluting," the mayor's office said, and had been identified as "the cause of many problems in the public space".
Quoted in the statement, Hidalgo said the fee increase would be "very significant". She did not, however, give a figure, or say what weight threshold would make an SUV "heavy".
If the vote goes in favour of the fee hike, it would not concern SUV owners with residential parking permits issued by the city.
The mayor's office said it hoped to send "a message" to auto companies inciting them to stop "their race to gigantism that is unsuitable to quality of life in the city".
This, it said, would "allow an improved sharing of public spaces in favour of clean mobility, streets with schools and pedestrians".
SUVs accounted for 49 percent of new passenger car sales in the European Union last year, according to the European Automobile Manufacturers' Association.
In April, Parisians voted overwhelmingly to banish for-hire electric scooters from the streets of the French capital. Turnout for the referendum was 100,000, representing just under 7.5 percent of the capital's registered voters.
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