In John 2:1-2, we read (emphasis added):
And the third day there was a marriage in Cana of Galilee; and the mother of Jesus was there: And both Jesus was called, and his disciples, to the marriage.
Commenting on the text in bold, John Tvedtnes wrote:
Though some Latter-day Saints have suggested that the event described here was Jesus’ wedding (based on the fact that the bridegroom was thanked for providing more wine in vv. 9-10), the fact that he was “called” (invited) mitigates against this. During their 1972 visit to Israel, President Harold B. Lee and Elder Gordon B. Hinckley discussed this topic among themselves and concluded that this was not Jesus’ marriage. An early third-century LAT preface to the text identifies the bridegroom as one of Jesus’ disciples, John, son of Zebedee, and indicates that his mother, Salome, was Mary’s sister—making John and his brother James cousins to Jesus. This would certainly explain why Jesus’ family was invited to the wedding. Salome was with Mary at the cross and at the tomb (Mark 15:40; 16:1), which again might suggest a family relationship. If John was Jesus’ cousin, this would also explain why, while hanging on the cross, he asked John to care for his mother (John 19:26-27). (Footnotes to the Study of the New Testament for Latter-day Saints, Volume 1: The Gospels, ed. Kevin L. Barney [2007], p. 492 note D)
For an interesting text on the debate about Jesus and whether he was married, see Anthony Le Donne, The Wife of Jesus: Ancient Texts and Modern Scandals