The gospels don’t publish the specific menus offered at any of Jesus’ meals, except for giving multiple references to him eating bread, very commonly imbibing wine, and a couple of times eating fish. Many people think it is improbable that Jesus was a vegetarian given the fact that he was an observant Jew of his time. Jewish dietary laws (a.k.a. kosher food laws) did not require, nor even encourage, vegetarianism. On the contrary, the Hebrew Scriptures command very particular ways of preparing and eating both sheep and goat meat, as well as other types of animal flesh. Going on this assumption then, we would guess that when Jesus’ family celebrated the Passover, for example, he would have eaten his share of the lamb. Scripture scholars generally hold the view that if there were particularly unusual attributes of Jesus — like being a vegetarian — they would have been noted in Scripture.
However, there are opposing views (such as the one espoused by jesusveg.com), which suggest that there were vegetarian Jews of Jesus’ time and that Jesus was one of them. Some Jews and Christians today do choose to eat a vegetarian diet as an outward manifestation of their faith and ethical values.
So a statement that “Jesus was a vegetarian” certainly can’t be proven, but it can’t be entirely ruled out either.