Karachi police chief Tariq Jamil said the bomb – left on a sidewalk – hit a vehicle carrying employees of the Jamiya Rashdiya Islamic seminary, run by the religious charity al-Rashid Trust which is believed by Pakistani officials to be close to hardline groups.
The dead man was an electrician who had been travelling with them, he said.
Three of the injured are in serious condition, a senior police official said.
No one has claimed responsibility for Saturday's blast.
Al-Rashid Trust operated several offices and relief centres in Afghanistan under the rule of the Taliban movement. Pakistan froze the bank accounts of al-Rashid Trust as part of a post 9/11 crackdown on private religious groups.
"We are investigating but we do not know the motives behind the attack," Jamil said.
Senior police investigator Fayyaz Leghari said the vehicle was targeted by a remote-control bomb.
"Those who planted the bomb knew when the vehicle would pass by the point," he said.
Witnesses said the teachers' van hit another car coming from the opposite direction after the explosion.
Karachi, Pakistan's commercial hub, is frequently hit by attacks, which have left 4000 people dead in the past five years.
Scientist set free
Meanwhile, the Pakistani government has released three persons detained in connection with the nuclear-technology proliferation scandal, including an aide to the "father" of the country's atomic bomb, Abd Al-Qadir Khan, Aljazeera's correspondent in Islamabad reports.
Abd Al-Qadir Khan is regarded as
the father of Pakistan's A-bomb
Nuclear scientist Nazir Ahmad Khan; Major Islam al Haq, principal staff officer of Abd Al-Qadir Khan; and Brigadier Sajawal Khan, security officer at the Khan Research Laboratories in Kahuta, were among the several people detained by the authorities for questioning at the beginning of the year in connection with the reported proliferation of Pakistani nuclear technology to Iran, Libya and North Korea.
The freed men have submitted a written promise to the government not to discuss the government's investigation even with their families and friends, Aljazeera's correspondent said.