The fact is there is no biblical record of a prophecy saying Jesus would be called a Nazarene yet Matthew quotes it.    He may have had in mind the quote from Isaiah 11:1  referring to a Root of Jesse and a Branch  (Hebrew word is nazer) sounds like nazarite. He shall be called a 'branch' might be what Matthew had in mind. 

He also wrote that is fulled by the 'prophets' (pl) so it might be a lot of differing prophecies that he fit together.   I am not sure and not a lot of scholars are sure what Matthew meant most think he was trying to make every prophecy fulfilled in Jesus.  Not sure.

 

“It is a necessary basic assumption of biblical interpretation that attention to the plain meaning of the text is the door to healthy understanding of the Bible.” (Paul S.Karleen Ph.D.)