They are both "correct". They just have a difference of nuance.
I must have dialled the wrong number implies that you didn't think you had, but obviously you "must have" done so because the person you wanted wasn't there. It's an expression of surprise and a tacit protestation that you thought you were dialling the wrong number.
I have dialled the wrong number is just a statement of fact. It is saying that you dialled the wrong number, without really any nuance or anything. It might be used when you realise that you really did dial the wrong number, that you made a mistake (reading the wrong line of your address book, for instance).
However, the nuance changes when they are prefaced with I'm sorry. If the apology is a distinct clause, the original difference applies - you are saying that you are sorry, and that you (must) have dialled the wrong number.
I'm sorry, I must have dialled the wrong number.
I'm sorry, I have dialled the wrong number.
Those would be more natural/usual, in my experience, than the alternative:
I'm sorry I must have dialled the wrong number.
I'm sorry I have dialled the wrong number.
Because there is no separation of clauses, the "I (must) have dialled the wrong number" becomes a modifier of "I'm sorry", which would be taken as showing what you are sorry about. You not apologising and stating that you dialled the wrong number, you are apologising for dialling the wrong number. This is valid and 'correct', but not usual - at least not in terms of what you say to the person who picked up the phone.
Also, the have isn't necessary in the version without the must. The simple past works just as well. If you want to use the perfect, it would be usual in most dialects that I'm familiar with to contract the "I have" to I've.
So, use the comma after sorry and then use must or not depending on what you are trying to say or indicate.