What is the grammar of the verb 'dare' in the following example?
The pizza was nice but, dare I say it, the salad was awful.
Is it some type of imperative?
Dare (like need) is a semi-modal verb, which means that in certain environments (see Negative Polarity), of which Yes/No Questions are one, dare may be used as a modal auxiliary verb.
If you substitute any other modal for dare in the sentence, you'll see what I mean:
These aren't all idioms like dare I say, and of course they don't mean the same, but they illustrate how modals work in questions. The only unusual thing is using dare as a modal verb here.
The statement "I dare (to) say it" one would expect to become a question as "Do I dare say it?" (and I would not object to that) ... But--as noted by John Lawler--"dare" is sometimes an auxiliary verb, and then it doesn't need the "do" so we can have "Dare I say it?". The other examples, "can, might" are auxiliary verbs only, so they will always act like this, and we CANNOT make questions like "*Do I can say it?" or "*Do I might say it?"