The short answer, according to the venerable language academy that advises on the proper use of Italian, is: both.
Though the term Covid-19 should really be feminine, it's so widely referred to as masculine by now that it's too late to correct it, the Accademia della Crusca says.
While 'il coronavirus' is definitely masculine, like any variations of the word 'virus' in Italian, 'Covid-19' is in fact an acronym for the respiratory illness the virus causes: 'COronaVIrus Disease (20)19'.
The Italian Health Ministry's FAQs refer to Covid-19 as feminine.
Since practically all the words you could use to translate 'disease' into Italian – malattia, infezione, patologia, sindrome – are feminine, Covid-19 should by rights be feminine too, the Florence-based Accademia says in its newly published 3,000-word opinion on the matter.
But probably because people mistakenly use the terms 'coronavirus' and 'Covid-19' interchangeably, the disease has commonly come to be called 'il virus Covid-19' or 'il Covid' in Italian – not only by journalists, but even on occasion by the Italian Health Ministry, the Accademia points out.
A warning to travellers from the Italian Health Ministry, referring to 'il Covid-19'.
In fact 'il Covid' is so ubiquitous by now that there's little hope of rectifying the mistake: “The masculine is now so firmly rooted in spoken Italian that even if linguists recommended the feminine it would probably have little effect,” the academy admits.
“The use of Covid in the masculine cannot therefore be considered grammatically incorrect,” it allows, even if “it would perhaps have been preferable” that Italians had adopted 'la Covid' from the start.
“All that remains is to recommend that the acronym at least be used consistently, especially within the same text,” the linguists resign themselves to saying.
In other words: pick 'il Covid' or 'la Covid' and stick to it.
The Italian language police are less dogmatic on the matter than their French counterparts, who ruled that the coronavirus is masculine, Covid-19 is feminine and saying otherwise constitutes “faulty use”.