The Quran makes the following statements about the Injil:
And in their footsteps, We sent 'Iesa (Jesus), son of Maryam (Mary) confirming the Taurat (Torah) that had come before him, and We gave him the Injeel (Gospel), in which was guidance and light and confirmation of the Taurat (Torah) that had come before it, a guidance and an admonition for Al-Muttaqun (the pious - see V.2:2). S. 5:46 Al-Hilali & Khan; cf. S. 57:27
He [Jesus] said, "Lo, I am God's servant; God has given me the Book, and made me a Prophet." S. 19:30 Arberry
It is He Who has sent down the Book (the Qur'an) to you (Muhammad SAW) with truth, confirming what came before it. And he sent down the Taurat (Torah) and the Injeel (Gospel). S. 3:3 Al-Hilali & Khan
Sura 5:46 states that the Injil was given to Jesus by Allah. Sura 19:30 and 3:3 then clarify that the Injil is a book just as the Qur'an and the Torah are books that were sent down by Allah.
The Qur'an also contains a second set of statements regarding the Injil:
Let the people of the Injeel (Gospel) judge by what Allah has revealed therein. ... S. 5:47 Al-Hilali & Khan
Say: "People of the Book, you do not stand on anything, until you perform the Torah and the Gospel [Injil], and what was sent down to you from your Lord." ... S. 5:68 Arberry
Those who follow the messenger, the Prophet who can neither read nor write, whom they will find described in the Torah and the Gospel [Injil] (which are) with them. S. 7:157 Pickthall
[Say (O Muhammad SAW)] "Shall I seek a judge other than Allah while it is He Who has sent down unto you the Book (The Qur'an), explained in detail." Those unto whom We gave the Scripture [the Taurat (Torah) and the Injeel (Gospel)] know that it is revealed from your Lord in truth. So be not you of those who doubt. S. 6:114 Al-Hilali & Khan
These verses make clear that the Injil is the book of the Christians, the book that is with them and which they believe in. The author of the Qur'an even admonishes the Christians to fully obey (the Torah and) the Injil that they have.
The Contradiction
However, here is the problem: when we look at the New Testament, the book which is the Scripture of the Christians, we see that it nowhere makes the claim that it is a book that was "given to Jesus". On the contrary, the New Testament consists of several books that were written by followers of Jesus (under the inspiration of the Holy Spirit) AFTER the ascension of Jesus.
Therefore, the Injil can EITHER be a book given to Jesus, OR it can be the book that the Christians hold as they Holy Scriptures, but it cannot be both. Muhammad apparently assumed that the Scripture of the Christians (and Jews) would be very similar to the Qur'an, the book which he thought he received from Allah. However, Muhammad was clearly ignorant of the matter. The essential nature of the Qur'an and the Bible are very different. A book "given to Jesus" in a similar way as Muhammad claims to have received the Qur'an does not exist and Christians have never claimed that such a book existed at any time. This claim of S. 5:46 is merely a wrong idea that sprang from the mind of Muhammad.
Had the author of the Qur'an made only statements like those found in S. 5:46 and 19:30, it might have been an option for Muslims to claim that the Injil of Jesus was simply lost. Jesus indeed received such a book but, somehow, it disappeared. Muslims could have said that the NT clearly is something very different from the Injil as defined by the Qur'an, and could have concluded that therefore they do not believe in the Christian New Testament since the Qur'an does not endorse it.
However, the second set of statements above prevents this explanation. The Qur'an identifies the Injil as the Scripture of the Christians. Thus, since the Injil is the book of the Christians, the Qur'an makes a blatantly wrong claim about the basic nature of the Injil. It neither is nor ever was a book given to Jesus.
The Source?
How could this error arise in the mind of Muhammad? He may have heard statements like in the first verse of the Gospel according to Mark:
The beginning of the gospel of Jesus Christ, ...
and mistakenly thought that this meant the same as "the Torah of Moses" i.e. a revelation given to a prophet in form of a book. However, reading the context shows that it means "this is the beginning of the Gospel ABOUT Jesus Christ"; the Gospel is the message telling us about the life and teaching of Jesus, written up by his followers, not a book given to Jesus himself.
Muhammad projected his own experience of receiving revelation of a book (the Qur'an) on Jesus and simply assumed that the book OF Jesus that was held sacred by his followers must also have been a book given TO Jesus (like the sacred book of the Muslims is the book given TO Muhammad). However, Muhammad was wrong about this, and this mistake exposes the Qur'an as a forgery. The Qur'an is not divine revelation but a collection of mistaken assumptions by its author.
But the Bible is corrupted!
In most cases when the Qur'an contradicts the Bible, Muslims shout, "but the Bible is corrupted", as if that is the answer and solution to every such problem.
There are at least two reasons why this response will not solve the problem.
First, the Qur'an never claims that the Injil is corrupted. There are certain accusations against the Jews, but no charge that the Christians corrupted their Scripture. The section, What the Qur'an says about the Bible, investigates this matter closely and shows that the Qur'an does not support the Muslim claim of Bible corruption.
Second, even if there had been some corruption of certain passages, small changes resulting in certain shifts of meaning, this cannot possibly explain the above contradiction in the Qur'an. Here we have a fundamental difference in the nature of the book which cannot be accounted for either with gradual changes or with a sudden change.
For illustration: The Qur'an is (allegedly) a book that was "sent down" from Allah to Muhammad. It was (supposedly) not written by Muhammad but given to him by Allah. On the other hand, the Hadith are memories of the companions and followers of Muhammad, formulated and written up by Muslims long after the death of Muhammad. They are their recollection of what Muhammad said and did.
Would it be possible for anyone to change the Qur'an (the book given to Muhammad) into a collection of hadiths without the Muslim community realizing that their scripture had changed into something entirely different?
Without doubt, the Muslim answer will be a resounding NO. But if that is impossible for the Muslim book and community, why would any Muslim think that this would have been possible in the Christian community? Originally, the Christians had a "book given to Jesus" but one day they woke up and their scripture had turned into a collection of writings by followers of Jesus and nobody realized the change, and nobody protested against it? Believing such a theory demands a lot of blind faith in the Qur'an. It is impossible. Anyone with the least bit of common sense will have to conclude that this cannot possibly have happened, and this implies that the author of the Qur'an simply made an error regarding the nature of the Christian Scripture.
Further reading
Contradictions in the Qur'an
The Incoherence of the Qur'an
Answering Islam Home Page