Will there be animal sacrifices in the Millennial Kingdom?

According to Ezekiel’s description of the temple in chapters 44-46, there will be sacrifices in the Millennial temple. There will be sacrifices which serve to commemorate the Passover, the Sabbath and other feasts. Of these feasts, only one will be required of Gentiles, the Feast of Tabernacles. We read this in Zechariah 14:

Zech. 14:16  Then it will come about that any who are left of all the nations that went against Jerusalem will go up from year to year to worship the King, the Lord of hosts, and to celebrate the Feast of Booths. 
Zech. 14:17 And it will be that whichever of the families of the earth does not go up to Jerusalem to worship the King, the Lord of hosts, there will be no rain on them. 
Zech. 14:18 If the family of Egypt does not go up or enter, then no rain will fall on them; it will be the plague with which the Lord smites the nations who do not go up to celebrate the Feast of Booths. 
Zech. 14:19 This will be the punishment of Egypt, and the punishment of all the nations who do not go up to celebrate the Feast of Booths.  

A failure to obey this requirement brings a punishment of plagues and drought, indicating that some nations will continue to rebel against the Lord in the Kingdom. 

The sacrifices of the Kingdom are part of a Kingdom Law which is different than the Law of Moses. The Law of Moses ended with the death of Christ, but the Kingdom Law will be instituted in the Kingdom. This law as explained in Ezekiel 40-43 includes animal sacrifices similar to the Law of Moses though different in some ways.

Just as the Old Testament sacrifices did not remit for sin, nor will the Kingdom sacrifices serve as a means to righteousness or forgiveness of sins. Rather, these rituals are a means of restoring fellowship for sinners living in the Kingdom and will also serve as a memorial of Jesus' redemptive work in the prior age. 

Remember, every age since Israel's formation has included a temple and a sacrificial service. Even in the age of the Church, there is a temple on earth and a sacrifice. The Bible says that the temple today is found in the body of all believers:

Eph. 2:19 So then you are no longer strangers and aliens, but you are fellow citizens with the saints, and are of God’s household,
Eph. 2:20 having been built on the foundation of the apostles and prophets, Christ Jesus Himself being the corner stone,
Eph. 2:21 in whom the whole building, being fitted together, is growing into a holy temple in the Lord,
Eph. 2:22 in whom you also are being built together into a dwelling of God in the Spirit.

And today there is a sacrifice for the Lord, as Paul explains:

Rom. 12:1  Therefore I urge you, brethren, by the mercies of God, to present your bodies a living and holy sacrifice, acceptable to God, which is your spiritual service of worship. 

For a more detailed explanation of the Kingdom life and temple service, please listen to our Revelation Bible study, especially Lessons 20B & C.