Memorizing music is an important aspect of learning any musical instrument. While I personally don't require students to memorize every single piece they learn, I do feel that memorization skills are necessary for any aspiring musician. Everyone who plays music should have some solos in their memory vault that they can pull out at a moment's notice - we don't want to go through our performance careers tethered to sheet music. Teaching students exactly how to memorize can be challenging, as each person learns in a unique way. Shadow practicing is one way to rehearse the music from memory without your instrument. Martha Beth Lewis provides some excellent tips on memorizing music as well. (Although written for pianists, the techniques can easily be applied to string players!)

Again, everyone learns differently, so it's important for individuals to figure out what methods work best for them. Also, it's never too soon to begin memorizing music. It's easiest to practice these techniques on simpler pieces first rather than pulling them out when tackling your first concerto.