The question roots from this question on ELL and the comment there down my answer.
Wait a minute ~ sounds fine
But then, how is wait for a minute
is different?
Also, if 'minutes are already described', dropping 'for' is okay in AmE and BrE as the comments there say:
10 minutes have passed, wait five more
I have strong feeling that it should have the preposition 'for'
10 minutes have passed, wait for five more.
I think you can drop 'for' if you are telling that instantly, probably with some caution (as in: wait a minute, I think I heard someone crying) BUT use 'for' if it is to describe the 'span' of time (as in: wait for five minutes, I'll be back).
The verb 'wait' is transitive and intransitive but in this context, I think mostly we use it as intransitive with no direct object? I'm not sure; will be happy to learn.
Best Answer
This is pretty generic and informal and is often used idiomatically to ask someone to pause what they're doing until told to continue. It doesn't usually mean exactly a minute, any more than "wait a second" means exactly a second.
This sounds like something that you'd find in directions/instructions:
In this case, it more often means exactly a minute, though it's not required. The exact timing here is more important. You would be unlikely to find native speakers who would use this in the idiomatic manner of the previous example.
Now, does this carry over to numbers of minutes greater than one? Sort of?
Will usually mean five actual minutes... otherwise, why bother specifying the number. As mentioned before, "wait a minute" doesn't really mean a minute... one could end up waiting for a few seconds or several minutes in the end. Even in directions, you'll often find they've left out the "for" in this case:
So what about with the "for"?
This isn't wrong. Using it this way is not ungrammatical at all, it's your choice. It's not required and you will definitely find examples of it, particularly in more professionally-written instructions:
This is also discussed, though not to a great degree, in Cambridge Dictionaries Online: