The girl, who has no criminal record, was detained at her home on Thursday, after an anti-terror raid near Paris.
She was an administrator of a group on the encrypted app, and is alleged to have been calling for attacks. The app had been used by the men who killed a priest in Normandy last month.
Thursday's raid was the result of monitoring by security services of suspicious behaviour on social networks, Le Parisien newspaper reports.
They noticed the thread where a few dozen members discussed so-called Islamic State (IS) propaganda, including calls to carry out attacks and videos, the newspaper said.
Investigations revealed the group administrator to be a 16-year-old secondary-school pupil.
"She relayed numerous Islamic State group propaganda messages calling for attacks, and she also expressed her own intention of taking action," a source close to the investigation told AFP news agency.
The security forces raided her family home in Melun, south-east of Paris, but found no explosives or firearms there, and took her into custody.
The investigators said the girl was "extremely radicalised" and was the administrator of the chat group dedicated to so-called Islamic State propaganda on the app, deputy prosecutor Laure Vermeersch said late on Monday.
The girl - whose name has not been released - did not mention any specific targets, Ms Vermeersch said. She is being investigated for "criminal terrorist enterprise" and "provocation to commit terrorist acts using online communication".
On 26 July, two 19-year-olds stormed a church in Saint-Etienne-du-Rouvray, a suburb of Rouen, during Mass and slit the throat of an elderly priest before being killed by police.
One of them is said to have sent out encrypted audio messages on Telegram, proclaiming his intention of carrying out an attack, days before the pair struck.
France has lived under a state of emergency since jihadist attackers killed 130 people last November in Paris.
Parliament extended the measure for an additional six months after the lorry attack in the southern city of Nice that killed 85 people on Bastille Day last month.
Separately, Mourad Hamyd, the brother-in-law of Cherif Kouachi, one of the perpetrators of the attack against Charlie Hebdo in Paris in 2015, has said he agrees to be extradited to France from Bulgaria, AFP reports.
Mr Hamyd was arrested by the Bulgarian authorities on 28 July after being stopped from entering Turkey; he is believed to have wanted to join IS in Syria, reports say.
Source: BBC News