The deceased was identified as Sharmin Akhter Liza, 16, a student of Konabari Cambridge College and daughter of Shafiqul Islam of Ambagh area in the city.
Locals caught the alleged killer -- Mostakin Rahman Raju, 17, a student of Lincoln Memorial College and son of Abul Kashem of Salna in the city, red-handed and handed him over to police.
Officer-in-charge of Konabari Police Station Md Emdad Hossain said Sharmin was returning home from her college after attending an examination.
On her way back, Raju obstructed her near Lincoln Memorial College around 2:30pm and proposed her which she rejected.
Angered at the refusal, Raju stabbed the girl with a knife indiscriminately, leaving her severely injured.
Locals rushed her to a hospital where doctors declared her dead.