It's not past perfect. It's present perfect with an auxiliary.
Why is "have" used? Well, "must left" would be incorrect. The other option would be "must leave," but that would change the meaning.
This particular "must" is used to express probability.
He must be in his twenties.
This means that he is probably in his twenties. There is a reason for me to suspect that he is most likely in his twenties. Because I am referring to a present state, I use the basic form of the main verb.
I must have left it at home.
Here, the thing that is likely is that I left it at home, so I'm referring to the past. So I need to use the perfect form to express that