The victim's condition was critical and she was undergoing treatment at Rao Tula Ram hospital in south Delhi, police said.
On Tuesday, around 4.00 pm, the couple met in a park in Dwarka area in south Delhi to sort out their differences over some issue. They left for home on motorbike but another round of argument ensued between them on the way.
"The girl was talking over the phone when the boy asked about the person whom she was talking to. The girl refused to divulge the caller's identity which infuriated the boy," police said.
"In the meantime, he stabbed her two or three times on the face and neck with a knife and ran away on his motorbike."
Some passersby saw the girl bleeding and called up the police.
Police said the boy had been arrested from his home in Najafgarh area, where the girl also lives in the neighbourhood.
He told police that he was angry over the girl's talking to their common friend which he did not like.