Officials said the incident took place when the girl and her three friends, bound for Srinagar, landed at the airport from Dhaka via Kolkata about 11:00 AM.
They said security agencies at the airport were alerted by some staff that a paper slip stating "carrying bomb" was in the baggage of the girl.
She was later detained and questioned by Delhi Police officials and central security agencies and the other three girls decided to stay put till their friend is cleared.
"Delhi Police released her after few hours of questioning. However, between all this, the girls missed their connecting flight to Srinagar from Delhi and will now take a flight tomorrow," an official said.
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Meanwhile, former Jammu and Kashmir Chief Minister Omar Abdullah took to Twitter and sought help from Prime Minister Narendra Modi and Home Minister Rajnath Singh in this regard.
"@HMOIndia @PMOIndia kindly look into the matter of the detention of two Kashmiri girls at Delhi airport. Their parents are very concerned.
The Home Minister promptly responded with the tweet "@abdullah_omar please send the details to pstohm@nic.In."
He said the grounds of their detention seem "filmsy".
"@HMOIndia @PMOIndia The grounds, as explained to me seem rather flimsy given that they flew from Dhaka to Delhi via Kolkata & then detained," Omar tweeted.
The parents of the girls said that four girls were returning home from Bangladesh when police at the airport detained them.
"There were four girls who were returning from Bangladesh. They flew from Dhaka to Kolkata and then to Delhi. Their luggage was checked and cleared at all the airports," Bilal Ahmad, the father of a detained girl, said in Srinagar.
He said the families tried to reach Chief Minister Mehbooba Mufti but were not granted a meeting with her.