The answer is at Acts 15:28,29, but the context is important in order to understand why it answers your question.
The book of Acts chronicles the development of the early Christian congregations following the death of Jesus. The first-century Christian congregations comprised of some Jewish Christians (Jewish persons who had responded to Jesus' teaching and become Christian) as well as those from many other nationalities and backgrounds, those whom Jews at the time would have called 'gentiles'.
Paul's letter to the Galatian congregation mentions 'Judaizers' - Christians who were still adhering to aspects of the Jewish law and, evidently, trying to force other non-Jewish Christians to follow it, too. In particular, the Jewish law on circumcision was being taught as still necessary, but Paul made it clear that it was no longer a requirement of God (see Galatians chapter 5).
It was in response to this matter of what, if any, aspects of the Jewish law should still apply to Christians that prompted the apostles to write at Acts 15:28,29:
The Holy Spirit has shown us that we should not place any extra burden on you. But you should not eat anything offered to idols. You should not eat any meat that still has the blood in it or any meat of any animal that has been strangled. You must also not commit any terrible sexual sins. If you follow these instructions, you will do well. (Contemporary English Version)
Inspired by the Holy Spirit, they determined that the Jewish law should no longer "burden" anyone, except the points that they went on to list which were all found in the law: (i) eating food offered to idols, (ii) eating blood, or strangled animals, which would contain blood as a consequence of that, (iii) sexual immorality. They showed that was an exhaustive list by concluding "if you follow these instructions, you will do well".
So those three aspects of the Jewish law are the only requirements for Christians today (in addition to Christ's teaching, of course), and that would mean that the festivals were not a requirement either. There is no historical evidence that the early Christians continued to celebrate those things.
As further evidence, remember also that the last night of Jesus life was the Passover. At the 'last Passover', Jesus instituted a new ceremony involving the Passover bread and wine, which he then instructed his apostles to "keep doing". So the Passover was clearly replaced by something new for Christians, giving further evidence that the festivals in the Jewish law are no longer a requirement for them.