This is mentioned in Luke 24:46.
… and [Jesus] said to them, “Thus it is written, that the Christ should suffer and on the third day rise from the dead.”
1 Corinthians 15:3-4 may also imply such as prophecy:
3 For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, 4 that he was buried, that he was raised on the third day in accordance with the Scriptures.
However, there is no prophecy that says the Messiah would rise on the third day. Several solutions to this problem have been proposed.
Some people have suggested that this is a reference to Hosea 6:1-2.
“Come, let us return to the Lord;
for he has torn us, that he may heal us;
he has struck us down, and he will bind us up.
2 After two days he will revive us;
on the third day he will raise us up,
that we may live before him.
While the context of this passage is clearly referring to Israel, it is possible that Jesus is teaching that Israel was foreshadowing what would happen to him.
Others have seen an allusion to Jonah as a type of symbolic prophecy. Jonah was in the fish for three days and three nights (Jonah 1:17; Matthew 12:40).
Still others have seen a reference to Isaac being released from death on the third day (Genesis 22:4), with Isaac being a type of Christ.
Possibly, Jesus referred to all three of these passages in explaining the Old Testament background to his resurrection on the third day.