backpack in the Vatican

Before entering the exhibition spaces, visitors are required to leave in the cloakroom all luggage, suitcases, rucksacks, packages and containers not considered suitable by staff on account of their size or nature.
Visitors who continue their tour in the Vatican Basilica are reminded not to leave their baggage in the Vatican Museums.
The cloakroom service is free of charge.

Here are all the regulations on the official Vatican Museum website
http://www.museivaticani.va/content/museivaticani/en/visita-i-musei/consigli-utili.html

How big?

https://www.rei.com/product/111161/rei-co-op-flash-45-pack

Probably not

http://www.eddiebauer.com/product/stowaway-packable-20l-daypack/82300168?showProducts=&sizetype=&size=

Unless packed full, this likely OK.... it was for me a few years back, but was only quarter or so filled; (water bottles guide book snacks)

Here is a more detailed list of items with the size limits for backpacks (rucksacks) - from their website.

Vatican Museum web site says "rucksacks" need to be left in the cloakroom. I guess third party tour operators may have their own rules, too.

Link to Vatican Museum website

Vatican Museum web site says "rucksacks" need to be left in the
cloakroom.

To be more specific, "rucksacks, with the possible exception of small ones that, when carried on the shoulders, do not exceed the widest point of the body by more than 15 cm". If it might be helpful, google up some pix of tourists in the Vatican Museums: you'll get an idea of the sorts and sizes of packs they're shouldering. Still, the smaller, the better, and "food and drinks of any type" are not allowed.

To be honest, I don't know how comfortable I'd be in the jostling, shoulder-to-shoulder crush with a backpack.

Simple answer, NO !!