The incident took place on the escalator of the Karkardooma Metro Station at 12:10 pm.
The deceased has been identified as Deepti. Pawan, the accused, fled the scene after leaving the 12 bore double barrel gun at the spot.
Deepti and her father Bisham Das were entering the Metro through an escalator when Pawan allegedly opened fire.
Five empty cartridges were recovered from the spot.
This is the second firing incident in the capital today.
Earlier in the day, a local BSP leader was shot dead by two unidentified assailants in South Delhi.