Baby Jesus is in Grand Army Plaza’s manger with the Virgin Mary and the shepherds and the NYPD out back.

Across New York City, cops are guarding Christmas trees, Nativity scenes and other public holiday displays, stepping up round-the-clock efforts to deter terrorism, vandalism, pickpocketing and youthful mischief, the department’s top spokesman said on Christmas Eve.

“We can’t just place cops on every tree and decoration,” said Deputy Commissioner for Public Information Stephen P. Davis, “but the places that are more prominent” are getting “special attention” from the 35,000-member police force.

Barricades surround the manger and lit-up Christmas tree at Grand Army Plaza in Brooklyn, keeping the public several feet from the attraction. At least one — and sometimes two — police officers are stationed under the nearby arch, a Civil War memorial dating to the 19th century.

Such patrols have been increased this season for Christmas and Hanukkah around the city where lots of people gather, including at Rockefeller Center, where the NYPD helps supplements security, said Davis, a department spokesman.

Earlier this month, police arrested a 14-year-old boy who allegedly twice toppled a menorah near Gracie Mansion, the mayoral residence, on Manhattan’s Upper East Side. The accused vandal told investigators he knocked over the 100-pound Hanukkah candelabrum because he was bored.

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Police also are at the holiday hot spots to combat petty theft like pickpocketing, Davis said.

“You got a lot of people gawking at a tree,” Davis said, creating an opportunity for thieves to steal from people focused on the Yuletide displays.

Davis said the police patrols at religious displays are aimed at deterring terrorist attacks like those earlier this year in Paris and San Bernardino, California, which killed dozens. But it’s also run-of-the-mill crime the police are trying to stop, such as youths’ vandalism.

“These kids sometimes just do these things,” he said. And it can be for more nefarious reasons, the police said.

“It’s a symbolic target,” Davis said.

About 11 years ago, a Jesus sculpture was stolen — twice — from St. Anthony of Padua Church in SoHo. In 2013, someone plucked Baby Jesus from a Nativity display at Sacred Hearts of Jesus and Mary-St. Stephen Catholic Church in Brooklyn — the same day a ceramic Baby Jesus was snatched from Our Lady Queen of Martyrs Catholic Church in Forest Hills, Queens.