Least crowded month for Vatican Museums?

Probably January, after Epiphany, on a midweek day. Dont expect no crowds, just somewhat lesser crowds.

Generally Nov to end of March (unless Easter falls at the end of March), is off season. Christmas/New Year’s holidays, including up to Epiphany on Jan 6, excluded of course, although I visited it right after Christmas many years ago and it wasn’t too bad then. January and February are the best to avoid crowds, if you don’t mind the colder temperatures.

January and February are the best to avoid crowds,

As I mentioned above, the last time we visited in February it was packed. If Jan and Feb are the best, either our last Feb visit was an aberration or there's no longer any reasonable time to visit.

Mornings have been consistently worse for us. It was nice when they allowed tours before official opening, but now there's just the Key Masters tour, which is great but goes too quickly.

I was there last week - it was packed at 10.00 am. Unless you pay for a very early morning tour with special access, I think it will be packed whenever you go.

The museums were very crowded in early March 2022. I think the situation is always pretty grim. If you haven't seen the museums during the peak travel months, you will not realize the conditions at other times could be worse. But they could be.

I've seen recommendations here for visiting the museums at times of Papal audiences at St. Peter's, because those special activities attract some of the people who would otherwise be at the museums.

In my experience the crowds were thinning out somewhat in the late afternoon, but it takes a lot of time to see the Vatican Museums, so just going for the last hour or so isn't a good solution for most people. Maybe if you only care about the Sistine Chapel, but the Chapel is the most crowded spot, so it will still be mobbed.

There are no longer affordable (under-150-euro) tours offering access to the Vatican Museums before they open to the public. The museums now open at 8 AM.