The girl in the video, Ahed Tamimi, 16, is not new to this kind of encounter.

Two years ago she was videotaped biting the hand of another Israeli soldier who was trying to arrest her brother. And in 2012, when she was 11, she was photographed raising her fist and yelling at another Israeli soldier — an action that earned her an award from Turkey.

That her family appears to encourage the children’s risky confrontations with soldiers offends some Palestinians and enrages many Israelis.

“We should exact a price at some other opportunity, in the dark, without witnesses and cameras,” the columnist Ben Caspit wrote. “The Tamimi family has to learn, the hard way, that such systematic provocations” come at great cost.

But Ms. Tamimi’s face has already launched a thousand memes, and the Tamimis of Nabi Saleh and their frequent videos have drawn international attention to their tiny village and its long-running disputes with a nearby Israeli settlement, Halamish, that Nabi Saleh residents say has stolen their land and water.

The latest incident, filmed in the family’s backyard, occurred within hours after a cousin of Ms. Tamimi’s was shot in the face with a rubber bullet, and it was streamed live on Facebook on Dec. 15. It first gained attention on Monday, when a clip was broadcast on Israeli television.

Right-wing activists demanded the teenager’s arrest. Israel’s education minister, Naftali Bennet, said Ms. Tamimi and the other women who scuffled with the soldiers alongside her — her mother and an older cousin — “should finish their lives in prison.”

By Tuesday morning, Ms. Tamimi was in custody; the other two were arrested later. A hearing on her case is set for Sunday.