Although it's not completely required, I would highly recommend playing Ocarina of Time first. Like Jedi said before, while it's not necessary, there are multiple references to Ocarina in Majora's Mask. Being a parallel universe, there are many characters that are carried over from Ocarina, as well as several other tidbits.
Pretty much, play through Ocarina first. You don't need to, but you'll find that Majora's Mask is more enjoyable if you do. You'll also look at some of the things in it and say, "Hey, I remember that from the last game", which makes it overall very satisfying.