Police said that the arrested person, identified as Tirath Singh, had allegedly kidnapped the girl on July 3.
The decomposed body of the girl was recovered on Saturday in the bushes near Nalthi Park.
Police suspect the minor might have been raped before she was killed.
The appearance of the body had sparked protests amongst locals here who slammed the Doda district administration for failing to prevent crimes against women.
Police said that a few protesters were arrested today during demonstrations in Bhaderwah where a bandh was observed over alleged lawlessness in the area.