The relic was donated by St. Sophronius, Patriarch of Jerusalem to Pope Theodore I in (642-649 CE).
After night fell, the traditional lighting of the Christmas tree ceremony was under way as hundreds gathered at Manger Square to celebrate the start of holiday season.
Crowded in a richly decorated suitcase, the crowds greeted the relic with great fanfare before she entered the Franciscan Church of St. Catherine near the Church of the Nativity of Christ, a holy place in the West Bank, where, according to legend, Jesus was born. This is to secure our existence as Christians in Bethlehem.
"We are excited and thank the pope, the holy father, Francis, for the gift and the right to safeguard the holy relic", Francesco Patton, Custos of the Holy Land for the Catholic church, said in a statement.
Palestinian Authority President Mahmoud Abbas had asked to borrow the entire manger, but the pope made a decision to send a tiny portion of it to stay permanently in Bethlehem, the custodian of the Franciscan order in the Holy Land, Brother Francesco Patton, told the Associated Press.
The relic was welcomed in the city some 1,400 years after it is said to have left the Holy Land.
The tiny piece of wood was preserved in an ornate silver cross displayed next to the altar.
Its arrival will coincide with Advent, a four-week period leading up to Christmas.
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The relic of the manger is not the first religious artefact to be returned by the Pope.
Earlier this year, the pontificate also gave bone fragments believed to be relics of Saint Peter to the Eastern Orthodox Church, an effort of goodwill his Orthodox counterpart called a "grand, fraternal and historic gesture", according to the Catholic News Service. He later said the move was meant to bring the Orthodox and Catholic churches together.
The rest of what is believed to be left of the manger is kept at the Basilica of Santa Maria Maggiore in Rome.
Christians make up a small minority of Palestinians and Bethlehem is one of the only cities in the West Bank and Gaza where Christmas is celebrated.
Yisca Harani, an Israeli expert on Christianity described the relic's return as an "inversion of history" Israeli newspaper Haaretz.
"A thousand years ago, Rome was busy collecting relics from the East to build itself up as an alternative Jerusalem".
Now the relic is to be installed "for ever" in Bethlehem, he said.