Yes. The Bible says that the spiritual gift of tongues (or languages) will cease. What is not so clear from the Scriptures is when this particular gift did or will stop.
Many Christians believe that this gift was given to authenticate the gospel and that the gift of tongues stopped after the apostles’ death and the completion of the New Testament documents. People who hold this belief are called cessationists because they teach that the miraculous gifts including tongues have ceased. On the other side of the debate are the continuationists who believe that the miraculous gifts have continued and are at least theoretically possible today.
The passage each side struggles with is 1 Corinthians 13:8.
Prophecy and speaking in unknown languages [in tongues] and special knowledge will become useless. But love will last forever! Now our knowledge is partial and incomplete, and even the gift of prophecy reveals only part of the whole picture! But when the time of perfection comes, these partial things will become useless.[1]
The primary question interpreters fight to answer is what the “perfect time” is that Paul is talking about. While the vast majority of pastors and theologians agree that the gift of tongues will pass away “when the time of perfection comes,” they don’t always agree on what inaugurates this time of perfection.
Those who believe that miraculous gifts stopped in the first century generally argue that the time of perfection began when the New Testament documents were completed. When the canon was closed, there was no longer any need for the miraculous gift of tongues.
On the other hand, those who believe that the miraculous gifts continued after the first century generally understand the time of perfection as Christ’s second coming. They teach that when Christ finally and fully reigns as king of the new heaven and new earth, all need for spiritual gifts like tongues, prophecy, and special knowledge will pass away. But until that time, God the Holy Spirit will use the gift of tongues as He sees fit.
[1] Tyndale House Publishers. (2007). Holy Bible: New Living Translation (3rd ed.) (1 Co 13:8–10). Carol Stream, IL: Tyndale House Publishers.