Luke 2:1-16: "In those days a decree went out from Caesar Augustus that all the world should be registered. This was the first registration when Quirinius was governor of Syria. And all went to be registered, each to his own town. And Joseph also went up from Galilee, from the town of Nazareth, to Judea, to the city of David, which is called Bethlehem, because he was of the house and lineage of David, to be registered with Mary, his betrothed, who was with child. And while they were there, the time came for her to give birth. And she gave birth to her firstborn son and wrapped him in swaddling cloths and laid him in a manger, because there was no place for them in the inn.
"And in the same region there were shepherds out in the field, keeping watch over their flock by night. And an angel of the Lord appeared to them, and the glory of the Lord shone around them, and they were filled with fear. And the angel said to them, 'Fear not, for behold, I bring you good news of great joy that will be for all the people. For unto you is born this day in the city of David a Savior, who is Christ the Lord. And this will be a sign for you: you will find a baby wrapped in swaddling cloths and lying in a manger.' And suddenly there was with the angel a multitude of the heavenly host praising God and saying, 'Glory to God in the highest, and on earth peace among those with whom he is pleased!'
"When the angels went away from them into heaven, the shepherds said to one another, 'Let us go over to Bethlehem and see this thing that has happened, which the Lord has made known to us.' And they went with haste and found Mary and Joseph, and the baby lying in a manger."
Isaiah 9:1-7: "But there will be no gloom for her who was in anguish. In the former time he brought into contempt the land of Zebulun and the land of Naphtali, but in the latter time he has made glorious the way of the sea, the land beyond the Jordan, Galilee of the nations.
"The people who walked in darkness have seen a great light; those who dwelt in a land of deep darkness, on them has light shined. You have multiplied the nation; you have increased its joy; they rejoice before you as with joy at the harvest, as they are glad when they divide the spoil. For the yoke of his burden, and the staff for his shoulder, the rod of his oppressor, you have broken as on the day of Midian. For every boot of the tramping warrior in battle tumult and every garment rolled in blood will be burned as fuel for the fire. For to us a child in born, to us a son is given; and the government shall be upon his shoulder, and his name shall be called Wonderful Counselor, Mighty God, Everlasting Father, Prince of Peace. Of the increase of his government and of peace there will be no end, on the throne of David and over his kingdom, to establish it and to uphold it with justice and with righteousness from this time forth and forevermore. The zeal of the LORD of hosts will do this."
The Luke text is the main referent for the hymn text, informing most of the first two verses. The conceit of the hymn is someone's visiting the manger after the shepherds ("Where shepherds lately knelt and kept the angel's word / I come in half-belief, a pilgrim strangely stirred"), so it's an imagined scenario rather than anything taken directly from the Bible.
The Isaiah text is referred to in the third verse. It's even mentioned specifically: "How should I not have known Isaiah would be there, / His prophecies fulfilled?" Later in the verse, Jesus is called "the Prince of Peace," a name that's also from Isaiah 9.
