The order, the military said, only applies to Israelis and not Palestinians.
A spokesperson said turning Taybeh into a closed military zone was "due to some violent attacks by Israelis in the region".
"Upon receiving any report of violations of the order, (Israel Defence Forces) soldiers are dispatched to the area and operate to disperse the gatherings and detain suspects in order to protect the citizens of the area and to maintain order," the military said in a statement.
Taybeh is one of the only Christian villages remaining in the West Bank and was visited last year by the Greek Orthodox patriarch and the Roman Catholic cardinal of Jerusalem.
It is also home to the Taybeh Brewing Co, widely considered the Middle East's oldest microbrewery.
Some Western countries have announced sanctions on settler groups over violent Israeli attacks on Palestinians.
In June, Israeli settlers obstructed Palestinians putting out a large blaze near Taybeh in the Israeli-occupied West Bank, according to Palestinian civil defence firefighters and a local priest who described an "ongoing pattern of intimidation and unjustified violence" that undermined the residents' fundamental rights.
A UN inquiry released on Tuesday found that Israeli authorities were directly involved in settler attacks that have killed, injured and displaced Palestinians in the West Bank.
Parts of Taybeh are located in Area B, where the Palestinian Authority runs civil administration but where security control must be coordinated with Israeli authorities.
The West Bank and Jerusalem are home to around 50,000 Palestinian Christians, members of a religious community there stretching back to antiquity in a region that is home to many of the faith's most important holy sites.
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