The teenager was detained on Tuesday during a search at his home, prosecutors in Duesseldorf said.
A court in nearby Leverkusen ordered him kept in custody on Wednesday on suspicion of planning and preparing a terror attack, they said in a statement.
The prosecutors said they could not give additional details for now.
The top regional security official, North Rhine-Westphalia state Interior Minister Herbert Reul, said the suspect had written in a chat group about attack plans and after a discussion of various scenarios, participants "agreed on a concrete plan to attack a Christmas market".
"It seemed very concrete," Reul told reporters of the alleged plan, about which he said he could not provide further details.
The boy's arrest came after German authorities received a tip from abroad about possible plans for an attack by a person in the region, according to Reul.
The authorities quickly identified the suspect, who was not previously known to local security authorities, he said.
There was a second arrest, in Brandenburg state in eastern Germany, the minister said but he could not give details about that.
Germany's domestic intelligence agency said earlier on Wednesday that the threat situation in the country has escalated since Hamas' October 7 attack in southern Israel.
The agency pointed to the risk of a radicalisation of lone assailants who use simple means to attack "soft targets," adding that "the danger is real and higher than it has been for a long time".
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