Amazingly, the idea of a the finality of revelation is not unique to the New Testament. When Peter makes the following statement he identifies two distinct classes of God's messengers,
"Remember the words spoken beforehand by the holy prophets and the commandment of the Lord and Savior spoken by your apostles." (2 Peter 3:1-2)
Beforehand, during the Old Covenant dispensation, the word of God was spoken by the holy prophets. Notice the past tense of this statement. As Peter writes this, the commandment of the Lord is spoken by the apostles. This was part of God's plan from the beginning. Consider the following two Old Testament prophecies from Daniel and Zechariah,
"Seventy weeks have been decreed for your people and your holy city, to finish the transgression, to make an end of sin, to make atonement for iniquity, to bring in everlasting righteousness, to seal up vision and prophecy and to anoint the most holy place. So you are to know and discern that from the issuing of a decree to restore and rebuild Jerusalem until Messiah the Prince there will be seven weeks and sixty-two weeks; it will be built again, with plaza and moat, even in times of distress." (Daniel 9:24-25)
We won't take a detailed look at this prophecy, as it is also examined in pages such as the survey of Messianic prophecy. But from simply reading these two verses the student can see that the end of sin, atonement for iniquity, everlasting righteousness, and the anointing of the most holy place happened during the time of Messiah the Prince. That is, at the cross. With that in mind, it is most logical to realize that sealing up vision and prophecy happened at precisely the same time. Regardless of how we calculate the weeks, there is a specific point in time, or at least a general point in time, when all six of these events took place. Thus we can conclude that if there is an end to sin, and if there is atonement for iniquity, and if there is everlasting righteousness, then vision and prophecy must be sealed up.
"Knowing this, that our old self was crucified with Him, in order that our body of sin might be done away with, so that we would no longer be slaves to sin." (Romans 6:6)
"And not only so, but we also joy in God through our Lord Jesus Christ, by whom we have now received the atonement." (Romans 5:11)
"But now apart from the Law the righteousness of God has been manifested, being witnessed by the Law and the Prophets." (Romans 3:21)
Yes, the deadly sting of sin is gone, we have received atonement for our iniquities, and the everlasting righteousness of God has been manifested. It is without question then, that vision and prophecy must also have been concluded in that generation. The prophet Zechariah corroborates this foretelling with another,
"In that day a fountain will be opened for the house of David and for the inhabitants of Jerusalem, for sin and for impurity. It will come about in that day," declares the LORD of hosts, "that I will cut off the names of the idols from the land, and they will no longer be remembered; and I will also remove the prophets and the unclean spirit from the land." (Zechariah 13:1-2)
That day clearly refers to the time of Christ when a fountain will be opened for the house of David. If there is any doubt one need only to read Zechariah chapter 12 and the context becomes clear. In that day there are three things that will happen. First, God's people will no longer worship idols; second, prophets will be removed; and third, unclean spirits will be expelled. Of interest to us is the second item - the removal of prophets.
Some say that this refers to false prophets, but there are two reasons this cannot be the case. Most obvious is that the text does not say false prophets. The Hebrew word for prophet is the same word used to describe God's messengers throughout scripture. Second, we can conclude through common sense that Zechariah cannot be describing false prophets. During his day, continuing through the time of Christ, and to this very day as we look into the Twenty-First Century, false prophets have always existed. If Zechariah was speaking of false prophets, then he himself is a false prophet, as his prophecy did not come true! Thus, we conclude that he can only be speaking of God's prophets of old and the conclusion of their role in God's plan.