The annual events are a huge tourist attraction during the Christmas season.
Initial reports following the mayor's press conference said the Christmas Market in Nazareth was cancelled.
Mayor Ali Salam pointed to Trump's December 6 decision to recognize Jerusalem as Israel's capital - which sparked violent protests and a call from Hamas for an uprising against Israel - as the reason for canceling all holiday plans. "The decision [by Trump to recognize Jerusalem] has taken away the joy of the holiday, and we will thus cancel the festivities this year".
He described his decision to recognize Jerusalem as the seat of Israel's government as merely based on reality.
The Brotherly Covenant, an NGO devoted to incorporating Christians into Israeli society, released a statement condemning the move and stated that cancelling Christmas in Nazareth would hinder chances at co-existence.
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"Today we finally acknowledge the obvious: that Jerusalem is Israel's capital", Mr Trump said in a speech in the White House last week.
Jerusalem holds significance for three major world religions - Islam, Judaism and Christianity.
Israeli Prime Minister Benjamin Netanyahu lauded the recognition as a "historic day" that is an "important step toward peace". Half of Jerusalem has been envisioned as the future capital of a Palestinian state, if a two-state solution is reached between Israel and Palestine. Trump stressed that he was not specifying the boundaries of Israeli sovereignty in the city, and called for no change in the status quo at the city's holy sites. Some 70 per cent of the population is Muslim and around 30 per cent are Christians, reflecting the importance of Nazareth to followers of that faith. "This shows the world that Jerusalem as the capital of Israel is not up for negotiation, and America is and shall always remain a loyal ally of Israel".
But the militant Palestinian group Hamas said Trump's decision "opens the gates of hell".
Nazareth as one of the holiest cities in Christendom because it was there that the angel Gabriel is believed by Christians to have told the Virgin Mary she would conceive and bear Jesus. The Christian savior also grew up in the town, according to the New Testament.