Pope Francis ordered the return of the thumb-sized relic from Rome's Basilica of Santa Maria Maggiore as a gift.
The relic had been in Rome since the 7th Century.
It was briefly put on display in Jerusalem before continuing its journey to Bethlehem to coincide with the start of Christmas celebrations there.
The relic, encased in an ornate stand, was welcomed to Bethlehem on Saturday by a procession of marching bands and taken to the Church of St Catherine, next to the Church of the Nativity where tradition says Jesus was born.
How important is the relic?
Christians believe the tiny piece of wood formed part of the crib that Jesus lay in after being born.
Custodia Terrae Sanctae, the custodian of Catholic religious sites in the Holy Land, said the Patriarch of Jerusalem, St Sophronius, donated the relic to Pope Theodore I in the 7th Century.
It said the relic had since been kept on display in Rome's Basilica of Santa Maria Maggiore, where a "very large number of pilgrims from all over the world" went each day to "venerate it".