"Are you hurt?" is grammatically correct. However, is it correct to ask someone in pain "Do you hurt?"?
Building on Joe's answer, grammatically, the "hurt" in
"Are you hurt?"
On the other hand, the "hurt" in
"Do you hurt?"
is just the bare infinitive of the intransitive verb "to hurt" (= to be in pain), used with the auxiliary "do" to form a present tense interrogative.
The verb "hurt" just happens to be irregular, such that its past participle looks identical to the bare infinitive. The grammar becomes clearer if we replace it with more regular verbs like, say, "injure" and "ache" (which also have the advantage that "injure" is always a transitive verb, whereas "ache" is generally intransitive):
"Are you injured?" (be + past participle)
"Do you ache?" (do + bare infinitive)
And yes, the past participle of English verbs behaves grammatically like an adjective, so it's also legitimate to analyze the first sentence as "Are you <adjective>?"
Indeed, several English adjectives (including, notably, the word "past" itself) started out as past participles of verbs, but later lost the connection with the original verb. This can happen because the verb itself has otherwise fallen out of use (for example, "crook" is rarely used as a verb any more, but "crooked" is still a perfectly good adjective) or because the original irregular participle has been replaced by a more regular one (as in "past" vs. "passed", or "wrought" vs. "worked").
Even when both the verb and its participle remain in common use, it's not unusual for the participle to acquire secondary meanings or connotations that don't directly map back to the verb. For example, off the top of my head, the adjective "baked", while clearly a regular past participle of the verb "bake", also has the slang meaning "high on marijuana" that doesn't correspond with any meaning of the original verb.
Arguably, this is somewhat true of "hurt", too — even though it's originally a past participle of a transitive verb, in common usage it doesn't really carry any connotation of there being an active agent that caused the injury. That is, you can be hurt (adjective = past participle) even if nobody has hurt (past tense) you.
The other answers are correct, but as a native speaker, I'd like to note that "Do you hurt?" may have unwanted connotations here. To me, it sounds like you're asking about a periodic or indefinite sort of pain, rather than an immediate and present pain (i.e. "Do you hurt often?" instead of "Are you in pain right now?). It also sounds more like emotional pain than physical pain.
But these are just my impressions. Other native speakers may interpret the question differently.
Either option is correct, but for a different meaning. The word "hurt" is doing two different tasks here.
"Hurt" in "Are you hurt?" is an adjective, meaning something like "injured", so you're basically asking "Are you injured?". In a sentence like this, you could use any adjective (though the meaning would be different). "Are you cold?", "Are you hungry?", etc.
"Hurt" in "Do you hurt?" is a verb, meaning something like "feel pain", so you're basically asking "Are you feeling any pain?". In a sentence like this, you could use any verb, ex: "Do you sing?", "Do you exist?", etc.
Perhaps I've lived an odd life, considering the various other responses not commenting on "Do you hurt?" sounding out of place, but that sentence, as is, sounds like a line from a book or a movie rather than a serious thing that someone would say to another person.
As noted by the others, the sentences mean the following:
Are you hurt?
Are you currently injured?
Do you hurt?
Are you in pain?
Both are grammatically correct, but while "Are you hurt?" is a fairly typical sentence to ask a person, "Are you in pain?" would be the more typical question to ask a person to ascertain whether they are currently in pain or not.
"Do you hurt?" sounds like a line that either a super-macho person would ask another super-macho person in an action film or perhaps what a person might ask someone else in Southern/Appalachian dialect, as in:
Do you hurt?
Yeah, I'm hurtin' real bad.
As mentioned by Kevin in comments, adding more to this sentence makes it far less unusual. His example is:
Do you hurt all over after that rugby match?
For what it's worth, I'm a native speaker, Midwestern US.
Note: I realize that the question only addressed whether the sentences were grammatically correct, but many people assume that a grammatically correct sentence is also going to be one that would be normal to use in conversation, thus this extended answer.
an adjective meaning "in pain"
a verb meaning "to be in pain" if used without an object.
- The subject can be an entire person - I'm hurting - or a body part - My hand hurts, my hand is hurting.
- It doesn't tend to mean one has sustained an injury, but is merely experiencing pain, especially when used in the progressive form.
- Because hurt works as an adjective, my hand is hurt, for example, is also a valid sentence.
a verb meaning "to cause pain or injury" if used with an object - I accidentally hurt Sally.
And Do you hurt? is a grammatical interrogative sentence that would take the second meaning above.
The difference between do you hurt? and are you hurt? - do you hurt assumes there is no visible injury and therefore you have to ask if the person is in pain, are you hurt would be if you haven't seen the person and are wondering if they sustained an injury.
The problem is the words "hurt" and "hurting" have very recently been used to replace the perfectly adequate words "suffer" and "suffering" (I would suggest for reasons of pretentiousness), for example instead of using the unambiguous statement "Joe is suffering since losing his job" certain people instead like to say "Joe is hurting since losing his job" which is very ambiguous as it equally implies "Joe is suffering" and "Joe is hurting others".
Up until the last few decades the actions associated with "hurt" and 'hurting" were always things one did to cause suffering in others, eg "Joe is hurting Jenny with verbal and physical abuse, poor Jenny is suffering." If "hurting" and "suffering" are accepted as synonyms then the word "hurting" will have two conflicting meanings. The simple solution is to always insist on the word "suffering" is used when they mean suffering.