The museum IS open on Mondays; also a crowded day as most other museums in Rome are closed on Monday. I suggest you go in the early afternoon if at all possible, when the line for tickets tends to be shorter. Or you can purchase a ticket in advance if you can pin down the time, thus avoiding a wait.
You can go to vatican.va to pre-purchase entrance tickets. This will also allow you to bypass any line to get into the museums.
Thanks for the info, we will buy tickets in advance for Monday.
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