The teenager has been detained for the offence that took place at Amlidihkala village under Chhuikhadan police station limits on Friday, the police said in a statement on Saturday.
The girl told the police that she and her brother (18) were at home at the time of the incident while the other family members had gone out for work.
Her brother reprimanded her claiming she talked to boys on mobile phone, and asked her not to use the phone anymore.
Angry over the rebuke, the girl allegedly hit her brother on his throat with an axe when he had fallen asleep. Her brother died on the spot, police said.
The girl then had a bath and cleaned the blood stains on her clothes before telling neighbours that her brother had been murdered.
After being alerted by villagers, a police team reached the spot and launched an investigation into the incident.
During questioning by police, the girl admitted to have killed him, the statement said.
A case was registered and further investigation was underway.