The Italian Grand Prix website (www.monzanet.it) said tickets would be fully refunded.
"The 2020 edition of the Italian Formula One Grand Prix at the Autodromo Nazionale Monza from 4-6 September will be held behind closed doors, that is without spectators," it added.
The blow is likely to be lessened, however, by Italy being handed three races this season for the first time -- the others being at Imola and Ferrari-owned Mugello, neither racetrack far from the team's Maranello factory.
Leclerc self isolating at home in Monaco after positive coronavirus test
Ferrari are also struggling this year, languishing fifth in the standings.
The first three races of the season that started this month in Austria have been held behind closed doors, with Britain's Silverstone hosting two more without spectators this weekend and next.
The Italian and British Grands Prix are the only races to have appeared on every calendar since the world championship started in 1950.
Monza, a temple to all things Ferrari, usually provides one of the sport's great atmospheres with the start-finish straight a sea of red after the race as fans flood the track to get close to the overhead podium.
Last year's race was won by Ferrari's young Monegasque Charles Leclerc.
Formula One is hoping to have spectators at other races in September and beyond, with tickets on sale for the Russian Grand Prix in Sochi.
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