Italian foreign minister Luigi Di Maio slammed the 10-second gag on the satirical Groland programme on Canal+, in which a coughing chef hacks up green phlegm onto the red tomato base and white mozzarella to make up the colours of the Italian flag.
Globally, more than 3,100 people have died of the coronavirus and over 90,000 have been infected.
In France there are now 204 confirmed cases and four people have died.
Italy is the worst-hit in Europe, with 52 deaths and over 2,000 people infected.
“Here's the new Italian pizza, which is going to spread around the world,” the fake advert says.
Countries from Britain to China and France have reported cases of people bringing the virus back with them from Italy.
“Making fun of the Italians like that, with the Coronavirus emergency we are facing, is profoundly disrespectful”, Di Maio said, adding that he had ordered the Italian embassy in Paris to voice Rome's displeasure.
He insisted the media were “morally obliged” not to spread disinformation, saying the Italian economy was paying the price.
The tourism sector in Italy has been hit particularly hard, with lots of airlines cutting or reducing flights to the north, where the outbreak is concentrated, and hotels reporting widespread cancellations while monuments and museums lie eerily empty.
Italy's agricultural minister Teresa Bellanova slammed the video as “shameful and horrifying”.
“This is not satire, it's an insult to an entire nation,” she said, demanding Canal+ apologise immediately.
“As the European and international authorities have repeatedly stated, it is not transmitted through food,” she said.
Despite that, Di Maio said unspecified countries had “called for a 'virus free' label on Italian products” – which was absurd.
The French joke also bombed with Italian farmers' association Coldiretti.
It slammed it a “stab in the back” for the Made in Italy industry, worth some €5 billion in exports to France, the second largest market after Germany.
The pestilent pizza ploy was a “petty and instrumental attack” on a market rival, it said.
The two countries historically compete on wine, cheese and bubbles, with Prosecco giving Champagne a run for its money.
The Alpine neighbours have long had turbulent relations.
The last time the neighbours swapped outright insults was under Italy's populist government, when political and diplomatic dialogue effectively ground to a halt.
But Di Maio opted on Tuesday for the moral high ground, inviting the video's makers “to come and eat pizza in Italy, a pizza like they have never eaten in their lives”.