The image depicted three people: a bloodied man labelled “Penne, tomato sauce”, a charred woman labelled “Crustes penne” and a collapsed building with battered limbs poking out entitled “Lasagne”.
Amatrice lawyer Mario Cicchetti filed the complaint on behalf of the town's local coucil in Rieti.
Mr Cicchetti told Italian news agency ANSA: “This is a macabre, senseless and inconceivable insult to victims of a natural event."
Italians had reacted to the cartoons with anger, and social media users described them as heartless" and "distasteful".
In response to the outcry Charlie Hebdo extended the unpopular joke by writing a message on their Facebook page stating: “Italians, it's not Charlie Hebdo that builds your homes, it's the Mafia!”
The Facebook post featured another cartoon depicting a bloodied and battered woman in the rubble with the same message.
Anti-Charlie Hebdo protests around the world
Show all 23
International opinion on Charlie Hebdo is mixed. In January 2015 the publication attracted global sympathy and was hailed as a bastion of free speech after Islamists stormed its Paris offices and killed 12 people.
Charlie Hebdo has not responded to a request for comment.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies