Witnesses and police officials said dozens more were injured, some seriously, in the blasts near an Islamic seminary in the troubled southern port city on Sunday.
"There was an explosion in a restaurant close to Jamia Binoria seminary which was followed by another big blast caused by a bomb fitted in a motorbike parked outside the restaurant," city police chief Fayyaz Leghari said.
An AFP correspondent saw the bodies of four seminary students in the port city's Abbasi Shaheed Hospital.
Doctor Syed Mazhar said two of the injured died in hospital.
A six-year-old child is also among the dead. Some of the injured are in critical condition, the doctor added.
Hayan Ahmed, 18, a religious student, said he was having tea at the restaurant when the first bomb went off and as he came out he was injured by the second blast.
Karachi, a teeming city of more than 14 million people, has been rocked by a spate of attacks since Pakistan joined the US-led war on terrorism in 2001.
Police blame extremists and al-Qaida-linked fighters for most of these attacks.
On Saturday, an explosion killed two people and wounded three others.